II. Convenient Short Tables

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The notation \Pxx " in a line represents a prime factor with xx decimal digits,

which are given explicitly in Appendix A. For example, the factorization of

2269 􀀀 1 is given as \269 13822297.P74" in the Short 2􀀀 table. The 74 digits of

the large prime factor may be found in Appendix A in the two lines which begin

\74 2,269􀀀". They appear as

6862 5988504811 7742593646

7066155294 8915363901 8450354163 7191246347 7873783063

When there are more factors than will _t on one line, the extra factors are given

on the next line (followed by the line number), the factorization being broken at a

multiplication dot, which is repeated on the second line. In Short 2+, for example,

the _nal two prime factors for line 210 are 146919792181 and 1041815865690181.

Note that we use a period rather than a centered dot for multiplication.

xi

Short 2􀀀

Factorizations of 2n 􀀀 1, n _ 400

n Prime Factors

2 3

3 7

4 3.5

5 31

6 3.3.7

7 127

8 3.5.17

9 7.73

10 3.11.31

11 23.89

12 3.3.5.7.13

13 8191

14 3.43.127

15 7.31.151

16 3.5.17.257

17 131071

18 3.3.3.7.19.73

19 524287

20 3.5.5.11.31.41

21 7.7.127.337

22 3.23.89.683

23 47.178481

24 3.3.5.7.13.17.241

25 31.601.1801

26 3.2731.8191

27 7.73.262657

28 3.5.29.43.113.127

29 233.1103.2089

30 3.3.7.11.31.151.331

31 2147483647

32 3.5.17.257.65537

33 7.23.89.599479

34 3.43691.131071

35 31.71.127.122921

36 3.3.3.5.7.13.19.37.73.109

37 223.616318177

38 3.174763.524287

39 7.79.8191.121369

40 3.5.5.11.17.31.41.61681

41 13367.164511353

42 3.3.7.7.43.127.337.5419

43 431.9719.2099863

44 3.5.23.89.397.683.2113

45 7.31.73.151.631.23311

xiii

Short 2􀀀 Prime Factors xiv

46 3.47.178481.2796203

47 2351.4513.13264529

48 3.3.5.7.13.17.97.241.257.673

49 127.443 2676798593

50 3.11.31.251.601.1801.4051

51 7.103.2143.11119.131071

52 3.5.53.157.1613.2731.8191

53 6361.69431.20394401

54 3.3.3.3.7.19.73.87211.262657

55 23.31.89.881.3191.201961

56 3.5.17.29.43.113.127.15790321

57 7.32377.524287.1212847

58 3.59.233.1103.2089.3033169

59 179951.320 3431780337

60 3.3.5.5.7.11.13.31.41.61.151.331.1321

61 230584300 9213693951

62 3.715827883.2147483647

63 7.7.73.127.337.92737.649657

64 3.5.17.257.641.65537.6700417

65 31.8191.14529 5143558111

66 3.3.7.23.67.89.683.20857.599479

67 193707721.76 1838257287

68 3.5.137.953.26317.43691.131071

69 7.47.178481.1005 2678938039

70 3.11.31.43.71.127.281.86171.122921

71 228479.48544121.212885833

72 3.3.3.5.7.13.17.19.37.73.109.241.433.38737

73 439.2298041.936 1973132609

74 3.223.1777.25781083.616318177

75 7.31.151.601.1801.100801.10567201

76 3.5.229.457.174763.524287.525313

77 23.89.127.58128364 3249112959

78 3.3.7.79.2731.8191.121369.22366891

79 2687.202029703.111 3491139767

80 3.5.5.11.17.31.41.257.61681.4278255361

81 7.73.2593.71119.262657.97685839

82 3.83.13367.164511353.8831418697

83 167.579 1261411327 5649087721

84 3.3.5.7.7.13.29.43.113.127.337.1429.5419.14449

85 31.131071.952097280 6333758431

86 3.431.9719.2099863.293 2031007403

87 7.233.1103.2089.4177.985 7737155463

88 3.5.17.23.89.353.397.683.2113.2931542417

89 6189700 1964269013 7449562111

90 3.3.3.7.11.19.31.73.151.331.631.23311.18837001

91 127.911.8191.112901153.2 3140471537

92 3.5.47.277.1013.1657.30269.178481.2796203

93 7.2147483647.65881228 8653553079

94 3.283.2351.4513.13264529.16 5768537521

95 31.191.524287.420778751.3 0327152671

96 3.3.5.7.13.17.97.193.241.257.673.65537.22253377

xv Prime Factors Short 2􀀀

97 11447.138426 0723582848 5645766393

98 3.43.127.436 3953127297.443 2676798593

99 7.23.73.89.199.153649.599479.3 3057806959

100 3.5.5.5.11.31.41.101.251.601.1801.4051.8101.268501

101 743 2339208719.34111753 1003194129

102 3.3.7.103.307.2143.2857.6529.11119.43691.131071

103 2550183799.39 7665642994 1438590393

104 3.5.17.53.157.1613.2731.8191.858001.308761441

105 7.7.31.71.127.151.337.29191.106681.122921.152041

106 3.107.6361.69431.20394401.2805 9810762433

107 162 2592768292 1336339157 8010288127

108 3.3.3.3.5.7.13.19.37.73.109.87211.246241.262657.279073

109 745988807.8700 3598609872 0987332873

110 3.11.11.23.31.89.683.881.2971.3191.201961.48912491

111 7.223.321679.26295457.319020217.616318177

112 3.5.17.29.43.113.127.257.5153.15790321.5 4410972897

113 3391.23279.65993.1868569.106681 8132868207

114 3.3.7.571.32377.174763.524287.1212847.160465489

115 31.47.14951.178481.4036961.264650 7710984041

116 3.5.59.233.1103.2089.3033169.107367629.536903681

117 7.73.79.937.6553.8191.86113.121369.7830118297

118 3.2833.37171.179951.1824726041.320 3431780337

119 127.239.20231.131071.6 2983048367.13 1105292137

120 3.3.5.5.7.11.13.17.31.41.61.151.241.331.1321.61681.4562284561

121 23.89.727.1 7863938783 6316422785 8270210279

122 3.76861433 6404564651.230584300 9213693951

123 7.13367.3887047.164511353.17772225 3954175633

124 3.5.5581.8681.49477.384773.715827883.2147483647

125 31.601.1801.26 9089806001.471088316 8879506001

126 3.3.3.7.7.19.43.73.127.337.5419.92737.649657.7 7158673929

127 170141183 4604692317 3168730371 5884105727

128 3.5.17.257.641.65537.274177.6700417.6728 0421310721

129 7.431.9719.2099863.110530 3606504929 4753459639

130 3.11.31.131.2731.8191.409891.7623851.14529 5143558111

131 263.10350794 4310551623 8671861923 7468234569

132 3.3.5.7.13.23.67.89.397.683.2113.20857.312709.599479.4327489

133 127.524287.163 5372208527 2539885143 4325720959

134 3.7327657.193707721.76 1838257287.671 3103182899

135 7.31.73.151.271.631.23311.262657.348031.4997 1617830801

136 3.5.17.17.137.953.26317.43691.131071.354689.287 9347902817

137 3203221559 6496435569.54 3904218360 0204290159

138 3.3.7.47.139.178481.2796203.16 8749965921.1005 2678938039

139 562 5767248687.1238761322 0520833576 2278423601

140 3.5.5.11.29.31.41.43.71.113.127.281.86171.122921.7416361.47392381

141 7.2351.4513.13264529.4375578271.64667503 5253258729

142 3.228479.48544121.56409643.212885833.1395 2598148481

143 23.89.8191.724153.15 8822951431.578217211 3400990737

144 3.3.3.5.7.13.17.19.37.73.97.109.241.257.433.577.673.38737.48 7824887233

145 31.233.1103.2089.2679 8951577838 6281469002 7494144991

146 3.439.1753.2298041.936 1973132609.179591803 8741070627

147 7.7.7.127.337.443 2676798593.27416 7236252872 5535068727

148 3.5.149.223.593.1777.25781083.184481113.231769777.616318177

Short 2􀀀 Prime Factors xvi

149 8665626856 6282183151.82351 0933669084 6723986161

150 3.3.7.11.31.151.251.331.601.1801.4051.100801.10567201.113 3836730401

151 18121.55871.165799.2332951.72890 8838338825 3664437433

152 3.5.17.229.457.1217.148961.174763.524287.525313.2451 7014940753

153 7.73.103.919.2143.11119.131071.755824 8842417934 7083438319

154 3.23.43.89.127.617.683.78233.3 5532364099.58128364 3249112959

155 31.31.311.11471.73471.2147483647.4649919401.1815 8209813151

156 3.3.5.7.13.13.53.79.157.313.1249.1613.2731.3121.8191.21841.121369.22366891

157 852133201.6 0726444167.165 4058017289.213438 7368610417

158 3.2687.202029703.111 3491139767.2014 8763660243 8195784363

159 7.6361.6679.69431.13960201.20394401.540701761.22 9890275929

160 3.5.5.11.17.31.41.257.61681.65537.414721.4278255361.4447 9210368001

161 47.127.1289.178481.3188767.4 5076044553.1480860771 5315782481

162 3.3.3.3.3.7.19.73.163.2593.71119.87211.135433.262657.97685839.272010961

163 150287.704161.110211473.2 7669118297.3623045457 0129675721

164 3.5.83.10169.13367.181549.12112549.43249589.164511353.8831418697

165 7.23.31.89.151.881.3191.201961.599479.20485 6883529738 0486760231

166 3.167.499.1163.2657.155377.1 3455809771.579 1261411327 5649087721

167 2349023.7963 8304766856 5073777786 1629608744 8490695649

168 3.3.5.7.7.13.17.29.43.113.127.241.337.1429.3361.5419.14449.15790321.8 8959882481

169 4057.8191.674 0339310641.3 3407622839 5239532950 6327023033

170 3.11.31.43691.131071.952097280 6333758431.2683142303 6065352611

171 7.73.32377.524287.1212847.93507247.30426 4563479254 1312037847

172 3.5.173.431.9719.101653.500177.2099863.175 9217765581.293 2031007403

173 730753.1505447.7008443 6712553223.1552 8574328857 2277679887

174 3.3.7.59.233.1103.2089.4177.3033169.985 7737155463.9607679 1871613611

175 31.71.127.601.1801.39551.122921.60816001.5353 4762479148 8552837151

176 3.5.17.23.89.257.353.397.683.2113.229153.119782433.2931542417.4 3872038849

177 7.179951.184081.2 7989941729.320 3431780337.921362408 4535989031

178 3.179.62020897.1858477 4046020617.6189700 1964269013 7449562111

179 359.1433.148945910 9360039866 4569401970 9543372166 4951999121

180 3.3.3.5.5.7.11.13.19.31.37.41.61.73.109.151.181.331.631.1321.23311.54001.

.18837001.29247661 180

181 43441.1164193.7648337.7923871 0972852956 2534464766 5764672671

182 3.43.127.911.2731.8191.224771.1210483.112901153.2 3140471537.2 5829691707

183 7.367.55633.230584300 9213693951.372017086 2530514630 3973352041

184 3.5.17.47.277.1013.1657.30269.178481.2796203.2912800 0924361888 8211558641

185 31.223.616318177.158785 5697992791.72488085 9928576000 1152755641

186 3.3.7.529510939.715827883.2147483647.2903110321.65881228 8653553079

187 23.89.131071.707983.103 2670816743 8438609988 5005627895 0666491537

188 3.5.283.2351.3761.4513.13264529.7484047069.16 5768537521.14073 7471578113

189 7.7.73.127.337.92737.262657.649657.1560007.2076174 8554425839 2970753527

190 3.11.31.191.2281.174763.524287.420778751.3 0327152671.301134747 9614249131

191 383.7068569257.3 9940132241.33258 4516519201.8727449712 4602996457

192 3.3.5.7.13.17.97.193.241.257.641.673.65537.6700417.22253377.

.1844674406 9414584321 192

193 13821503.616 5444023324 8340616559.147322653 2114531733 1353282383

194 3.971.1553.11447.31817.110087601 8364883721.138426 0723582848 5645766393

195 7.31.79.151.8191.121369.14529 5143558111.1343041968 4509926257 2814573351

196 3.5.29.43.113.127.197.1 9707683773.436 3953127297.443 2676798593.498 1857697937

197 7487.268288 0399791288 6929710867 0418919894 9048689384 5712448833

xvii Prime Factors Short 2􀀀

198 3.3.3.7.19.23.67.73.89.199.683.5347.20857.153649.599479.3 3057806959.

.24209 9935645987 198

199 16 4504919713.488416409 3883941177 6600490985 8632430297 7543600799

200 3.5.5.5.11.17.31.41.101.251.401.601.1801.4051.8101.61681.268501.340801.

.2787601.3173389601 200

201 7.1609.22111.193707721.76 1838257287.87 4494233974 2585794267 8833145441

202 3.743 2339208719.34111753 1003194129.8451004001 5215293433 1135470251

203 127.233.1103.2089.136417.121793911.11348055 5808832720 1109085605 3175361113

204 3.3.5.7.13.103.137.307.409.953.2143.2857.3061.6529.11119.13669.26317.

.43691.131071.1326700741 204

205 31.13367.2940521.164511353.7 0171342151.3 6557250655 0879718167 4078959681

206 3.2550183799.41 5141630193.814276708 1771726171.39 7665642994 1438590393

207 7.47.73.79903.178481.634569679.223 2578641663.1005 2678938039.4216 6482463639

208 3.5.17.53.157.257.1613.2731.8191.858001.308761441.789198817 2627109114 3763623681

209 23.89.524287.9480 3416684681.151234 8937147247.53469 5054132396 0232319657

210 3.3.7.7.11.31.43.71.127.151.211.281.331.337.5419.29191.86171.106681.

.122921.152041.664441.1564921 210

211 15193.6027295643 3838849161.3593875704 4958237573 8819989426 8773153439

212 3.5.107.6361.69431.15358129.20394401.586477649.2805 9810762433.180143 9824104653

213 7.66457.228479.48544121.212885833.284988197 2114740679.420526857 4191396793

214 3.643.841157474 4904788148 8635567801.162 2592768292 1336339157 8010288127

215 31.431.1721.9719.2099863.731516431.51 4851898711.2979272 8974404776 4444862191

216 3.3.3.3.5.7.13.17.19.37.73.109.241.433.38737.87211.246241.262657.279073.

.33975937.13899 1501037953 216

217 127.5209.62497.2147483647.62 6870393384 0364033151.3784 2880443142 4484082633

218 3.104124649.745988807.8700 3598609872 0987332873.20777 5684736234 8863128179

219 7.439.3943.2298041.936 1973132609.67116589 8617413417.48 1531461520 4347717321

220 3.5.5.11.11.23.31.41.89.397.683.881.2113.2971.3191.201961.48912491.

.41 5878438361.363 0105520141 220

221 1327.8191.131071.23654 5439841839 9772605086 2092143634 5855283986 6247069233

222 3.3.7.223.1777.3331.17539.321679.25781083.26295457.319020217.616318177.

.10777 5231312019 222

223 18287.196687.1466449.2916841.14 6949526239 8780123809.5962 4259998711 6128415063

224 3.5.17.29.43.113.127.257.449.2689.5153.65537.15790321.183076097.

.5 4410972897.35842 9848460993 224

225 7.31.73.151.601.631.1801.23311.100801.115201.617401.10567201.1348206751.

.1386136 9826299351 225

226 3.227.3391.23279.48817.65993.1868569.636190001.106681 8132868207.

.49100336 9344660409 226

227 2698633 3437777017.79 9217773820 5979626491 5069508677 2095354566 0121688631

228 3.3.5.7.13.229.457.571.32377.131101.160969.174763.524287.525313.1212847.

.160465489.27 5415303169 228

229 1504073.20492753.5983345 7464970183.467795120 1875837235 3428000034 8743236593

230 3.11.31.47.691.14951.178481.2796203.4036961.1884103651.34576 7385170491.

.264650 7710984041 230

231 7.7.23.89.127.337.463.599479.58128364 3249112959.

.4982 3976511782 5615133830 2204762057 231

232 3.5.17.59.233.1103.2089.59393.3033169.107367629.536903681.

.822801951 6714411983 2390568177 232

233 1399.135607.622577.1168681 2987907760 0270344856 3247662600 8506653285 3492178431

234 3.3.3.7.19.73.79.937.2731.6553.8191.86113.121369.22366891.7830118297.

.53 0230622637 0307681801 234

235 31.2351.4513.13264529.2391314881.7 2296287361.

.73202 3003951580 0584547353 7146974751 235

Short 2􀀀 Prime Factors xviii

236 3.5.1181.2833.3541.37171.157649.174877.179951.5521693.1824726041.

.10 4399276341.320 3431780337 236

237 7.1423.2687.49297.202029703.111 3491139767.2372882351 2345609279.

.3135737341 7090093431 237

238 3.43.127.239.20231.43691.131071.823679683.6 2983048367.13 1105292137.

.1 4316255316 5560959297 238

239 479.1913.5737.176383.134000609.

.711000871 7824458123 1050142792 5375409686 3768062879 239

240 3.3.5.5.7.11.13.17.31.41.61.97.151.241.257.331.673.1321.61681.394783681.

.4278255361.4562284561.4 6908728641 240

241 22000409.160619 4743723522 8941273750 8720216839 2258056563 2899087995 3332340439

242 3.23.89.683.727.117371.110541845 8279780045 5736061107.

.1 7863938783 6316422785 8270210279 242

243 7.73.487.2593.71119.262657.97685839.1675 3783618801.19297 1705688577.

.371299016 3251158343 243

244 3.5.733.1709.3456749.36 8140581013.66 7055378149.76861433 6404564651.

.230584300 9213693951 244

245 31.71.127.1471.122921.443 2676798593.

.25235990 2034571016 8562142988 5170852973 8525821631 245

246 3.3.7.83.739.13367.165313.3887047.164511353.8831418697.1319431 7913029593.

.17772225 3954175633 246

247 8191.15809.524287.645 9570124697.40200 4106269663.

.1282 8161176172 6506045349 6956212169 247

248 3.5.17.5581.8681.49477.290657.384773.715827883.2147483647.3770202641.

.11 4162918040 1976895873 248

249 7.167.1621324657.579 1261411327 5649087721.

.8241594690 1671373595 5227441843 2855740327 249

250 3.11.31.251.601.1801.4051.229668251.26 9089806001.471088316 8879506001.

.55 1948541833 6288303251 250

251 503.54217.1 7823028721 4063289511.616 7688219869 5257501367.

.120703 9617824989 3039969681 251

252 3.3.3.5.7.7.13.19.29.37.43.73.109.113.127.337.1429.5419.14449.92737.

.649657.4 0388473189.7 7158673929.11 8750098349 252

253 23.23.47.89.178481.4103188409.1999 5773632843 5366769577.

.44 6677117627 9779840303 9426178361 253

254 3.56713727 8201564105 7722910123 8628035243.

.170141183 4604692317 3168730371 5884105727 254

255 7.31.103.151.2143.11119.106591.131071.949111.952097280 6333758431.

.57024515 7763977554 5838643151 255

256 3.5.17.257.641.65537.274177.6700417.6728 0421310721.

.5964958 9127497217.57 0468920068 5129054721 256

257 53500 6138814359.11556 8539524661 9182673033.

.374550598 5018109365 8177663009 6313181393 257

258 3.3.7.431.1033.9719.2099863.1591582393.293 2031007403.1568 6603697451.

.110530 3606504929 4753459639 258

259 127.223.616318177.2499285769.

.212343 7096088009 8806027750 1855527137 0686697057 8963970119 259

260 3.5.5.11.31.41.53.131.157.521.1613.2731.8191.51481.409891.7623851.

.34110701.10814 0989558681.14529 5143558111 260

261 7.73.233.1103.2089.4177.985 7737155463.

.3 2801702501 4102923449 9886637529 6008088651 1412965881 261

262 3.263.1049.4744297.1823311286 8120778178 4391813611.

.10350794 4310551623 8671861923 7468234569 262

263 23671.1357 2264529177.1202263 6053684849 8024035943.

.383725 1266551709 6450131573 0676446647 263

264 3.3.5.7.13.17.23.67.89.241.353.397.683.2113.7393.20857.312709.599479.

.4327489.1761345169.2931542417.9 8618273953 264

xix Prime Factors Short 2􀀀

265 31.6361.69431.20394401.2 9324808311.19774 8738449921.

.36614110 1247352946 3443561902 7766763481 265

266 3.43.127.4523.174763.524287.1067882904 4384829528 4382097033.

.163 5372208527 2539885143 4325720959 266

267 7.78903841.2875 3302853087.6189700 1964269013 7449562111.

.24 1243324377 1392408426 7316537353 267

268 3.5.269.7327657.15152453.42875177.193707721.2559066073.76 1838257287.

.671 3103182899.973 9278030221 268

269 13822297.P74

270 3.3.3.3.7.11.19.31.73.151.271.331.631.811.15121.23311.87211.262657.

.348031.18837001.4997 1617830801.38583 8642647891 270

271 1 5242475217.

.24 8927757868 1318902773 3054156782 0045256364 2739707732 8654218838 6932989391 271

272 3.5.17.17.137.257.953.26317.43691.131071.354689.383521.236 8179743873.

.287 9347902817.3 7320072247 0799764577 272

273 7.7.79.127.337.911.8191.121369.108749551.112901153.2 3140471537.

.409320 4977277417.8697759580 1949844993 273

274 3.1097.15619.3212796 3626435681.10549821 2027592977.3203221559 6496435569.

.54 3904218360 0204290159 274

275 23.31.89.601.881.1801.3191.201961.3 8202766513 4363932751.

.4074891477 3548868150 3330808737 9995347151 275

276 3.3.5.7.13.47.139.277.1013.1657.30269.178481.2796203.16 8749965921.

.541 5624023749.1005 2678938039.7033 4392823809 276

277 1121297.31133636 3056102094 8220110905 0392404721.

.6955979459 7765400522 8093485158 9652278783 277

278 3.4506937.562 5767248687.1238761322 0520833576 2278423601.

.51542 6395246617 9530007417 4250365699 278

279 7.73.16183.34039.1437967.2147483647.83373 2508401263.65881228 8653553079.

.20344 3983695186 7299888617 279

280 3.5.5.11.17.29.31.41.43.71.113.127.281.61681.86171.122921.7416361.

.15790321.47392381.841798420 7765786201 1867889681 280

281 80929.P80

282 3.3.7.283.2351.4513.1681003.13264529.4375578271.3 5273039401.

.11 1349165273.16 5768537521.64667503 5253258729 282

283 9623.6 8492481833.

.2 3579543011 7989932228 5089392956 5870383844 1678738515 0267731105 7483194673 283

284 3.5.569.228479.48544121.56409643.148587949.212885833.4999465853.

.5585522857.47 2287102421.1395 2598148481 284

285 7.31.151.191.32377.524287.1212847.420778751.3 0327152671.

.14 9147703568 9218775711.253 4924298663 7720573561 285

286 3.23.89.683.2003.2731.8191.724153.6156182033.1 0425285443.15 8822951431.

.1550 0487753323.578217211 3400990737 286

287 127.13367.164511353.1 7137716527.

.51 9543908777 4865574425 6192963206 2209192728 9554884381 7842228913 287

288 3.3.3.5.7.13.17.19.37.73.97.109.193.241.257.433.577.673.1153.6337.38737.

.65537.22253377.3 8941695937.27 8452876033.48 7824887233 288

289 131071.12761663.1790 5831260439 2742511009.

.33 2093499435 6628805321 7335207909 4760898942 0068445023 289

290 3.11.31.59.233.1103.2089.3033169.7553921.9998028 5472471530 0883845411.

.2679 8951577838 6281469002 7494144991 290

291 7.11447.272959.2065304407.5434876633.138426 0723582848 5645766393.

.1170 7116447776 5187765955 6633665719 291

292 3.5.293.439.1753.9929.2298041.936 1973132609.64930 1712182209.

.179591803 8741070627.94 4473296560 1851473921 292

293 401223 6245561622 1971122353.

.396 6452270281 3889041561 1220710757 9216439107 4310303170 1971222447 293

Short 2􀀀 Prime Factors xx

294 3.3.7.7.7.43.127.337.5419.748819.436 3953127297.443 2676798593.

.2603288584 5392093851.27416 7236252872 5535068727 294

295 31.4721.132751.179951.5794391.128818831.3812358161.320 3431780337.

.45282 4604065751.44 1097523065 0827973711 295

296 3.5.17.149.223.593.1777.25781083.184481113.231769777.616318177.

.2098 8936657440 5864861512 6425661022 2593863921 296

297 7.23.73.89.199.153649.262657.599479.8950393.3 3057806959.

.17088661 8823141738 0818309508 0729277164 8313599433 297

298 3.1193.650833.38369587.8665626856 6282183151.82351 0933669084 6723986161.

.79845595 7350425985 6359124657 298

299 47.599.8191.178481.9341359.1 4718679249.1344447683 6590589479.

.5144156315 1591093599.2 6024244971 2509916159 299

300 3.3.5.5.5.7.11.13.31.41.61.101.151.251.331.601.1201.1321.1801.4051.8101.

.63901.100801.268501.10567201.13334701.1182468601.113 3836730401 300

301 127.431.9719.490631.2099863.3655 0582371197 8039310711.

.2033695 2491372732 4581005538 4288578491 9705927999 301

302 3.18121.55871.165799.2332951.1871 7738334417.72890 8838338825 3664437433.

.50 8340508241 0077967730 6460621499 302

303 7.607.743 2339208719.34111753 1003194129.

.15127682 2241373525 5864403005 2641058393 2437477852 0631853993 303

304 3.5.17.229.257.457.1217.27361.148961.174763.524287.525313.2451 7014940753.

.6939446 0463940481.116 9955781771 7358904481 304

305 31.1831.2441.4271.270841.48407 4637694471.230584300 9213693951.

.36 4371848053 9731284003 8029362441 7256758401 305

306 3.3.3.7.19.73.103.307.919.2143.2857.6529.11119.43691.123931.131071.

.2 6159806891.2743 9122228481.755824 8842417934 7083438319 306

307 14608903.85798519.2 3487583303.7 8952752017.

.1121774 7647447052 5577861298 9378353385 4572309313 4076373561 307

308 3.5.23.29.43.89.113.127.397.617.683.2113.8317.78233.869467061.3019242689.

.3 5532364099.7609 6559910757.58128364 3249112959 308

309 7.2550183799.19 5327276678 0718501831.39 7665642994 1438590393.

.7521737478 7325720535 8122784001 7636545169 309

310 3.11.31.31.311.11161.11471.73471.715827883.2147483647.4649919401.

.1815 8209813151.594760 3221397891.2912605 6043168521 310

311 5344847.2 6476493739 1020515846 8946067671.

.2948036 8134895929 6477194164 0646430621 8755953753 9328375831 311

312 3.3.5.7.13.13.17.53.79.157.241.313.1249.1613.2731.3121.8191.21841.121369.

.858001.22366891.308761441.841593759 4876209925 4554456081 312

313 10960009.1478797 0697180273.38571 9476428914 1165278097.

.2669301 2026551688 2861649499 5862048325 8358551879 313

314 3.15073.2350291.852133201.6 0726444167.165 4058017289.213438 7368610417.

.1775178 3757817897.9683329919 8971305921 314

315 7.7.31.71.73.127.151.337.631.23311.29191.92737.106681.122921.152041.

.649657.870031.983431.29 7283071559 6370681022 8435378401 315

316 3.5.317.2687.202029703.111 3491139767.3 8136461186 6507317969.

.2014 8763660243 8195784363.6044 6290980621 5075725313 316

317 9511.58749252 1482839879.48681 2267132209 8041565641.

.981563923 1755686605 0313174400 3116158457 2466128599 317

318 3.3.7.107.6043.6361.6679.69431.13960201.20394401.540701761.22 9890275929.

.2805 9810762433.44751303 6651810208 4427698737 318

319 23.89.233.1103.2089.18503.64439.8 4819793631.

.9609 3220390955 5426827710 7484843200 2182622501 5228170095 4275029793 319

320 3.5.5.11.17.31.41.257.641.61681.65537.414721.3602561.6700417.4278255361.

.4447 9210368001.94 4556849534 8456305599 1838558081 320

321 7.1786 6285599391.162 2592768292 1336339157 8010288127.

.2 1051680008 9955301807 2924887925 8818886965 0399862249 321

xxi Prime Factors Short 2􀀀

322 3.43.47.127.1289.178481.2796203.3188767.4 5076044553.1480860771 5315782481.

.8103467492 7597923271 4980036156 4410265219 322

323 647.7753.131071.524287.3904435878 8825633753.

.1 2696398284 5458876397 2435091645 2598691857 1846507555 0865591017 323

324 3.3.3.3.3.5.7.13.19.37.73.109.163.2593.71119.87211.135433.246241.262657.

.279073.3618757.97685839.106979941.168410989.272010961.4977454861 324

325 31.601.1801.7151.8191.5 1879585551.14529 5143558111.

.46136793 9193695361 0429590532 0141225322 6033973964 4049093601 325

326 3.150287.704161.110211473.1 1281292593.2 7669118297.102339 8150341859.

.3623045457 0129675721.3375 7054705039 0415041769 326

327 7.745988807.2059727673 4348736647.331 5702979495 9983067039.

.881 1616575406 1081804047.8700 3598609872 0987332873 327

328 3.5.17.83.10169.13121.13367.181549.12112549.43249589.164511353.8562191377.

.8831418697.12243 8641224656 1215510639 2056552353 328

329 127.2351.4513.12503.200033.9106063.13264529.270447871.

.99340183 7923042561 0659608142 8856937819 4109188864 7157503817 329

330 3.3.7.11.11.23.31.67.89.151.331.683.881.2971.3191.20857.201961.599479.

.48912491.415365721.225212 7523412251.20485 6883529738 0486760231 330

331 1693 7389168607.86511 8802936559.

.29 8542624980 1974636137 6721533356 9428005686 4688358212 5372179668 2625551919 331

332 3.5.167.499.997.1163.2657.155377.13063537.1 3455809771.4 6202197673.

.20 9957719973.14806719 7374074653.579 1261411327 5649087721 332

333 7.73.223.1999.10657.169831.321679.1238761.26295457.36085879.199381087.

.319020217.616318177.69 8962539799.409646055 9560875111 333

334 3.2349023.7963 8304766856 5073777786 1629608744 8490695649.

.6235740319 2785191176 6905528625 6140883865 3121833643 334

335 31.464311.193707721.1532217641.76 1838257287.

.21505 4093284059 2106005778 3156144213 6184854608 4491128444 8661782641 335

336 3.3.5.7.7.13.17.29.43.97.113.127.241.257.337.673.1429.2017.3361.5153.5419.

.14449.15790321.2 5629623713.5 4410972897.8 8959882481.153859 5959564161 336

337 18199.2806537.9 5763203297.72 6584894969.

.78778047 3264667429 9361242084 2416198311 3940080688 2247552723 9136925369 337

338 3.2731.4057.8191.674 0339310641.492991076 4223610387.

.185262386 4601108673 2742614043.3 3407622839 5239532950 6327023033 338

339 7.3391.23279.65993.1868569.10113049.106681 8132868207.

.3200216 2476840557 4452943847.4760 1379922835 9986081422 6997712217 339

340 3.5.5.11.31.41.137.953.1021.4421.26317.43691.131071.550801.23650061.

.722690435 2843746841.952097280 6333758431.2683142303 6065352611 340

341 23.89.2147483647.556012549 3425335999.1269 0114180536 9975317583.

.144421113 7344578755 4135614601 8455080327 6100931567 341

342 3.3.3.7.19.19.73.571.32377.174763.524287.1212847.93507247.160465489.

.30426 4563479254 1312037847.19 1774583879 4026811634 9766612211 342

343 127.6073159.1428389887.6 2228099977.443 2676798593.

.58 9618044748 4416472481 4095915114 3380931461 1824837521 3688557057 343

344 3.5.17.173.431.9719.101653.500177.2099863.3855260977.175 9217765581.

.293 2031007403.6408215 0767423457.14253 4327510312 6327372769 344

345 7.31.47.151.14951.178481.4036961.1005 2678938039.264650 7710984041.

.1623 8361411159 5675973306 3205096145 7324182993 2932497191 345

346 3.347.4153.730753.1505447.3 5374479827.4 7635010587.7008443 6712553223.

.1552 8574328857 2277679887.16434 6424772818 9221623609 346

347 141 4318911295 2632419639.P83

348 3.3.5.7.13.59.233.349.1103.2089.4177.29581.3033169.107367629.536903681.

.2 7920807689.985 7737155463.2217021 4192500421.9607679 1871613611 348

349 177 9973928671.34 7203962732 1265779992 0861294559.

.18 5553936486 3068386822 9284313709 3603368550 9547424669 1696225599 349

350 3.11.31.43.71.127.251.281.601.1051.1801.4051.39551.86171.110251.122921.

.60816001.34 7833278451.3401003 2331525251.5353 4762479148 8552837151 350

Short 2􀀀 Prime Factors xxii

351 7.73.79.937.6553.8191.86113.121369.262657.446473.29121769.7830118297.

.57189 0896913727.9371500 8807883087.1 5083242680 0173710177 351

352 3.5.17.23.89.257.353.397.683.2113.65537.229153.5304641.119782433.

.2931542417.4 3872038849.27 5509565477 8488426047 7762382801 1666349761 352

353 931921.2927 4554768003 0196411680 5545194017.

.6725414 7561119557 8150388018 8940925566 0519600395 7457367584 3402666863 353

354 3.3.7.2833.13099.37171.179951.184081.1824726041.2 7989941729.320 3431780337.

.445 3762543897.189868549 6465999273.921362408 4535989031 354

355 31.228479.48544121.212885833.12 1932688511.

.822 3125624363 2928398155 1459269790 5768406610 7973340993 8550717411 1379292321 355

356 3.5.179.1069.62020897.1858477 4046020617.5790 1779199499 9956106149.

.1237940 0392854506 4364330189.6189700 1964269013 7449562111 356

357 7.7.103.127.239.337.2143.4999.11119.20231.131071.6 2983048367.13 1105292137.

.2452 6224891371 5001137177.8 8894321245 9351249796 3252165417 357

358 3.359.1433.5 8745093521.434 7868190665 8793734959 5056277570 7707143803.

.148945910 9360039866 4569401970 9543372166 4951999121 358

359 719.855857.778165529.6587733 0027880703.370906 5807444927 8543029950 3112990447.

.100361196 2812937456 8252086186 0411315001 359

360 3.3.3.5.5.7.11.13.17.19.31.37.41.61.73.109.151.181.241.331.433.631.1321.

.23311.38737.54001.61681.18837001.29247661.4562284561.16 8692292721.

.46977549 5062434961 360

361 524287.952 2401530937.36 4505682067 7060879117 8096385783.

.258112211 7924395218 6920238827 4131312903 6848393342 8434308863 361

362 3.1811.43441.1164193.7648337.31675363.7923871 0972852956 2534464766 5764672671.

.1781 0163630112 6245793428 1173397808 5990447907 362

363 7.23.89.727.8713.599479.7593961.7 5824014993.1 7863938783 6316422785 8270210279.

.33569 4389427634 9540717714 2157304182 3051433281 363

364 3.5.29.43.53.113.127.157.911.1093.1093.1613.2731.4733.8191.224771.1210483.

.112901153.2 3140471537.2 5829691707.886108 5190774909.55633852 5912325157 364

365 31.439.8761.2298041.936 1973132609.1382 8603741081.8259 5052745831.

.256513 9526231840 7934919734 7817377970 6743128539 0452848441 365

366 3.3.7.367.55633.76861433 6404564651.230584300 9213693951.

.372017086 2530514630 3973352041.1772303 9943798878 2976979507 7302561451 366

367 12479.51791041.7813 8581882953.3013111165 4089911444 6723859201.

.197557 4008195191 0036006278 8275098751 2009286363 8283602681 367

368 3.5.17.47.257.277.1013.1657.30269.178481.2796203.4 3717618369.

.54967540 8461419937.39702 9956747290 2879791777.2912800 0924361888 8211558641 368

369 7.73.13367.3887047.164511353.637638 6802464073.17772225 3954175633.

.2429301 5036958172 5249341464 4754212492 0559238437 0695685937 369

370 3.11.31.223.1481.1777.25781083.28136651.616318177.158785 5697992791.

.72488085 9928576000 1152755641.778 4293653978 8760854061 8330873281 370

371 127.743.2969.6361.69431.20394401.6 3781899287.2 0471236659 7949333831.

.1459803 3715563444 4285232523 8769793184 5146475626 6456641329 371

372 3.3.5.7.13.373.5581.8681.49477.384773.529510939.715827883.2147483647.

.2903110321.95108 8215727633.65881228 8653553079.461154528 3086450689 372

373 25569151.P105

374 3.23.89.683.43691.131071.707983.103 2670816743 8438609988 5005627895 0666491537.

.219116582 5376888084 7501577164 2457906201 5865776131 374

375 7.31.151.601.751.1801.100801.10567201.26 9089806001.471088316 8879506001.

.21397310 2046405409 2520609592 4599407068 1827513979 3055476751 375

376 3.5.17.283.2351.3761.4513.13264529.1198107457.7484047069.2 3592342593.

.16 5768537521.14073 7471578113.450194 6625921233.1 8135230685 2476069537 376

377 233.1103.2089.5279.8191.148055441.359661017.P81

378 3.3.3.3.7.7.19.43.73.127.337.379.5419.87211.92737.119827.262657.649657.

.1560007.7 7158673929.12 7391413339.5620 2143607667.

.2076174 8554425839 2970753527 378

xxiii Prime Factors Short 2􀀀

379 18 0818808679.P103

380 3.5.5.11.31.41.191.229.457.761.2281.54721.174763.524287.525313.420778751.

.3 0327152671.27669663 1250953741.241692362 0660807201.301134747 9614249131 380

381 7.2287.15241.349759.170141183 4604692317 3168730371 5884105727.

.339 2128785962 1179611077 0323541353 2814941272 8532035452 4672773903 381

382 3.383.7068569257.3 9940132241.33258 4516519201.8727449712 4602996457.

.10461836 2256444679 3972631570 5346110693 5039257407 7339085483 382

383 1440847.7435494593.5038230 4420458112 9045587727.

.15174 9235586808 1261681843 6353130417.

.240522700 2351678934 9690025659 9634325263 383

384 3.3.5.7.13.17.97.193.241.257.641.673.769.65537.274177.6700417.22253377.

.6728 0421310721.1844674406 9414584321.442499 8269453035 9355647316 4314770689 384

385 23.31.71.89.127.881.3191.55441.122921.201961.197 1764055031.58128364 3249112959.

.310553 4168119044 4478126719 7559651345 7115147392 5765532041 385

386 3.6563.13821503.35679139.1871670769.745509 9975844049.

.12 8076133738 8845898643.616 5444023324 8340616559.

.147322653 2114531733 1353282383 386

387 7.73.431.9719.2099863.11492353.2276 3003975641.68340 4033534957 8249140287.

.110530 3606504929 4753459639.3 5489505810 9826355908 4652467359 387

388 3.5.389.971.1553.3881.4657.5821.11447.31817.3555339061.4959325597.

.39 4563864677.1763 7260034881.110087601 8364883721.

.138426 0723582848 5645766393 388

389 56478911.4765678679.P100

390 3.3.7.11.31.79.131.151.331.2731.8191.107251.121369.409891.7623851.22366891.

.14529 5143558111.5714 0392112607 6957182161.1343041968 4509926257 2814573351 390

391 47.37537.131071.178481.2580624 8225716242 8454918322 4489963592 7231330561.

.47352 9906275104 7834629348 9474767666 4271002855 2319600543 391

392 3.5.17.29.43.113.127.197.7057.273617.1007441.15790321.375327457.1 9707683773.

.140 5628248417.436 3953127297.443 2676798593.498 1857697937.36456 5561997841 392

393 7.263.36093121.51118297.58352641.10350794 4310551623 8671861923 7468234569.

.98333 0461445530 2578430964 2808939555 1222341502 8355534287 393

394 3.7487.19 7002597249.134895935 2853811313.2519515738 6725301225 9144010843.

.268288 0399791288 6929710867 0418919894 9048689384 5712448833 394

395 31.2687.12641.202029703.5435488351.1 6203007441.111 3491139767.

.3868132159 6249165469 0527257306 3237265865 9771994032 1344865278 2202624081 395

396 3.3.3.5.7.13.19.23.37.67.73.89.109.199.397.683.2113.5347.20857.42373.

.153649.235621.312709.599479.4327489.3 3057806959.846 3901912489.

.1597 5607282273.24209 9935645987 396

397 2383.6353.50023.53993.202471.5877983.8141328728 0852258794 0886856743.

.1 2349042135 7600027254 2841146073.6 5974859102 7032651990 0042655193 397

398 3.16 4504919713.488416409 3883941177 6600490985 8632430297 7543600799.

.2678230073 7649837925 6993682056 8604337537 0049896379 8805883563 398

399 7.7.127.337.32377.73417.83791.524287.1212847.

.163 5372208527 2539885143 4325720959.

.297246 1473987634 4125010817 4337037758 7796038883 8436140673 399

400 3.5.5.5.11.17.31.41.101.251.257.401.601.1601.1801.4051.8101.25601.61681.

.268501.340801.2787601.82471201.3173389601.4278255361.

.432 3632031270 0288550654 3172618401 400

Short 2+

Factorizations of 2n + 1, n _ 400

n Prime Factors

1 3

2 5

3 3.3

4 17

5 3.11

6 5.13

7 3.43

8 257

9 3.3.3.19

10 5.5.41

11 3.683

12 17.241

13 3.2731

14 5.29.113

15 3.3.11.331

16 65537

17 3.43691

18 5.13.37.109

19 3.174763

20 17.61681

21 3.3.43.5419

22 5.397.2113

23 3.2796203

24 97.257.673

25 3.11.251.4051

26 5.53.157.1613

27 3.3.3.3.19.87211

28 17.15790321

29 3.59.3033169

30 5.5.13.41.61.1321

31 3.715827883

32 641.6700417

33 3.3.67.683.20857

34 5.137.953.26317

35 3.11.43.281.86171

36 17.241.433.38737

37 3.1777.25781083

38 5.229.457.525313

39 3.3.2731.22366891

40 257.4278255361

41 3.83.8831418697

42 5.13.29.113.1429.14449

43 3.293 2031007403

44 17.353.2931542417

xxiv

xxv Prime Factors Short 2+

45 3.3.3.11.19.331.18837001

46 5.277.1013.1657.30269

47 3.283.16 5768537521

48 193.65537.22253377

49 3.43.436 3953127297

50 5.5.5.41.101.8101.268501

51 3.3.307.2857.6529.43691

52 17.858001.308761441

53 3.107.2805 9810762433

54 5.13.37.109.246241.279073

55 3.11.11.683.2971.48912491

56 257.5153.5 4410972897

57 3.3.571.174763.160465489

58 5.107367629.536903681

59 3.2833.37171.1824726041

60 17.241.61681.4562284561

61 3.76861433 6404564651

62 5.5581.8681.49477.384773

63 3.3.3.19.43.5419.7 7158673929

64 274177.6728 0421310721

65 3.11.131.2731.409891.7623851

66 5.13.397.2113.312709.4327489

67 3.7327657.671 3103182899

68 17.17.354689.287 9347902817

69 3.3.139.2796203.16 8749965921

70 5.5.29.41.113.7416361.47392381

71 3.56409643.1395 2598148481

72 97.257.577.673.48 7824887233

73 3.1753.179591803 8741070627

74 5.149.593.184481113.231769777

75 3.3.11.251.331.4051.113 3836730401

76 17.1217.148961.2451 7014940753

77 3.43.617.683.78233.3 5532364099

78 5.13.13.53.157.313.1249.1613.3121.21841

79 3.2014 8763660243 8195784363

80 65537.414721.4447 9210368001

81 3.3.3.3.3.19.163.87211.135433.272010961

82 5.10169.181549.12112549.43249589

83 3.499.1163.2657.155377.1 3455809771

84 17.241.3361.15790321.8 8959882481

85 3.11.43691.2683142303 6065352611

86 5.173.101653.500177.175 9217765581

87 3.3.59.3033169.9607679 1871613611

88 257.229153.119782433.4 3872038849

89 3.179.62020897.1858477 4046020617

90 5.5.13.37.41.61.109.181.1321.54001.29247661

91 3.43.2731.224771.1210483.2 5829691707

92 17.2912800 0924361888 8211558641

93 3.3.529510939.715827883.2903110321

94 5.3761.7484047069.14073 7471578113

95 3.11.2281.174763.301134747 9614249131

Short 2+ Prime Factors xxvi

96 641.6700417.1844674406 9414584321

97 3.971.1553.31817.110087601 8364883721

98 5.29.113.197.1 9707683773.498 1857697937

99 3.3.3.19.67.683.5347.20857.24209 9935645987

100 17.401.61681.340801.2787601.3173389601

101 3.8451004001 5215293433 1135470251

102 5.13.137.409.953.3061.13669.26317.1326700741

103 3.41 5141630193.814276708 1771726171

104 257.789198817 2627109114 3763623681

105 3.3.11.43.211.281.331.5419.86171.664441.1564921

106 5.15358129.586477649.180143 9824104653

107 3.643.841157474 4904788148 8635567801

108 17.241.433.38737.33975937.13899 1501037953

109 3.104124649.20777 5684736234 8863128179

110 5.5.41.397.2113.41 5878438361.363 0105520141

111 3.3.1777.3331.17539.25781083.10777 5231312019

112 449.2689.65537.183076097.35842 9848460993

113 3.227.48817.636190001.49100336 9344660409

114 5.13.229.457.131101.160969.525313.27 5415303169

115 3.11.691.2796203.1884103651.34576 7385170491

116 17.59393.822801951 6714411983 2390568177

117 3.3.3.19.2731.22366891.53 0230622637 0307681801

118 5.1181.3541.157649.174877.5521693.10 4399276341

119 3.43.43691.823679683.1 4316255316 5560959297

120 97.257.673.394783681.4278255361.4 6908728641

121 3.683.117371.110541845 8279780045 5736061107

122 5.733.1709.3456749.36 8140581013.66 7055378149

123 3.3.83.739.165313.8831418697.1319431 7913029593

124 17.290657.3770202641.11 4162918040 1976895873

125 3.11.251.4051.229668251.55 1948541833 6288303251

126 5.13.29.37.109.113.1429.14449.4 0388473189.11 8750098349

127 3.56713727 8201564105 7722910123 8628035243

128 5964958 9127497217.57 0468920068 5129054721

129 3.3.1033.1591582393.293 2031007403.1568 6603697451

130 5.5.41.53.157.521.1613.51481.34110701.10814 0989558681

131 3.1049.4744297.1823311286 8120778178 4391813611

132 17.241.353.7393.1761345169.2931542417.9 8618273953

133 3.43.4523.174763.1067882904 4384829528 4382097033

134 5.269.15152453.42875177.2559066073.973 9278030221

135 3.3.3.3.11.19.331.811.15121.87211.18837001.38583 8642647891

136 257.383521.236 8179743873.3 7320072247 0799764577

137 3.1097.15619.3212796 3626435681.10549821 2027592977

138 5.13.277.1013.1657.30269.541 5624023749.7033 4392823809

139 3.4506937.51542 6395246617 9530007417 4250365699

140 17.61681.15790321.841798420 7765786201 1867889681

141 3.3.283.1681003.3 5273039401.11 1349165273.16 5768537521

142 5.569.148587949.4999465853.5585522857.47 2287102421

143 3.683.2003.2731.6156182033.1 0425285443.1550 0487753323

144 193.1153.6337.65537.22253377.3 8941695937.27 8452876033

145 3.11.59.3033169.7553921.9998028 5472471530 0883845411

146 5.293.9929.64930 1712182209.94 4473296560 1851473921

147 3.3.43.5419.748819.436 3953127297.2603288584 5392093851

xxvii Prime Factors Short 2+

148 17.2098 8936657440 5864861512 6425661022 2593863921

149 3.1193.650833.38369587.79845595 7350425985 6359124657

150 5.5.5.13.41.61.101.1201.1321.8101.63901.268501.13334701.1182468601

151 3.1871 7738334417.50 8340508241 0077967730 6460621499

152 257.27361.6939446 0463940481.116 9955781771 7358904481

153 3.3.3.19.307.2857.6529.43691.123931.2 6159806891.2743 9122228481

154 5.29.113.397.2113.8317.869467061.3019242689.7609 6559910757

155 3.11.11161.715827883.594760 3221397891.2912605 6043168521

156 17.241.858001.308761441.841593759 4876209925 4554456081

157 3.15073.2350291.1775178 3757817897.9683329919 8971305921

158 5.317.3 8136461186 6507317969.6044 6290980621 5075725313

159 3.3.107.6043.2805 9810762433.44751303 6651810208 4427698737

160 641.3602561.6700417.94 4556849534 8456305599 1838558081

161 3.43.2796203.8103467492 7597923271 4980036156 4410265219

162 5.13.37.109.246241.279073.3618757.106979941.168410989.4977454861

163 3.1 1281292593.102339 8150341859.3375 7054705039 0415041769

164 17.13121.8562191377.12243 8641224656 1215510639 2056552353

165 3.3.11.11.67.331.683.2971.20857.48912491.415365721.225212 7523412251

166 5.997.13063537.4 6202197673.20 9957719973.14806719 7374074653

167 3.6235740319 2785191176 6905528625 6140883865 3121833643

168 97.257.673.2017.5153.2 5629623713.5 4410972897.153859 5959564161

169 3.2731.492991076 4223610387.185262386 4601108673 2742614043

170 5.5.41.137.953.1021.4421.26317.550801.23650061.722690435 2843746841

171 3.3.3.19.19.571.174763.160465489.19 1774583879 4026811634 9766612211

172 17.3855260977.6408215 0767423457.14253 4327510312 6327372769

173 3.347.4153.3 5374479827.4 7635010587.16434 6424772818 9221623609

174 5.13.349.29581.107367629.536903681.2 7920807689.2217021 4192500421

175 3.11.43.251.281.1051.4051.86171.110251.34 7833278451.3401003 2331525251

176 65537.5304641.27 5509565477 8488426047 7762382801 1666349761

177 3.3.2833.13099.37171.1824726041.445 3762543897.189868549 6465999273

178 5.1069.5790 1779199499 9956106149.1237940 0392854506 4364330189

179 3.5 8745093521.434 7868190665 8793734959 5056277570 7707143803

180 17.241.433.38737.61681.4562284561.16 8692292721.46977549 5062434961

181 3.1811.31675363.1781 0163630112 6245793428 1173397808 5990447907

182 5.29.53.113.157.1093.1093.1613.4733.886108 5190774909.55633852 5912325157

183 3.3.76861433 6404564651.1772303 9943798878 2976979507 7302561451

184 257.4 3717618369.54967540 8461419937.39702 9956747290 2879791777

185 3.11.1481.1777.25781083.28136651.778 4293653978 8760854061 8330873281

186 5.13.373.5581.8681.49477.384773.95108 8215727633.461154528 3086450689

187 3.683.43691.219116582 5376888084 7501577164 2457906201 5865776131

188 17.1198107457.2 3592342593.450194 6625921233.1 8135230685 2476069537

189 3.3.3.3.19.43.379.5419.87211.119827.7 7158673929.12 7391413339.5620 2143607667

190 5.5.41.229.457.761.54721.525313.27669663 1250953741.241692362 0660807201

191 3.10461836 2256444679 3972631570 5346110693 5039257407 7339085483

192 769.274177.6728 0421310721.442499 8269453035 9355647316 4314770689

193 3.6563.35679139.1871670769.745509 9975844049.12 8076133738 8845898643

194 5.389.3881.4657.5821.3555339061.4959325597.39 4563864677.1763 7260034881

195 3.3.11.131.331.2731.107251.409891.7623851.22366891.5714 0392112607 6957182161

196 17.7057.273617.1007441.15790321.375327457.140 5628248417.36456 5561997841

197 3.19 7002597249.134895935 2853811313.2519515738 6725301225 9144010843

198 5.13.37.109.397.2113.42373.235621.312709.4327489.846 3901912489.1597 5607282273

199 3.2678230073 7649837925 6993682056 8604337537 0049896379 8805883563

Short 2+ Prime Factors xxviii

200 257.1601.25601.82471201.4278255361.432 3632031270 0288550654 3172618401

201 3.3.2011.9649.6324667.7327657.671 3103182899.591515 4911853267 6874448563

202 5.809.9491060093.521 8735279937.60050 3817460697.5342503736 3873248657

203 3.43.59.3033169.596834617.3692022713.252 7158146155 6596241868 8965855731

204 17.17.241.8161.354689.40932193.146 7129352609.287 9347902817.73753 9985835313

205 3.11.83.8831418697.212582056 3389437533 3902438938 3459784675 7304863651

206 5.41201.17325013.520379897.47300015 7711296729.1170 7009745765 6623005977

207 3.3.3.19.139.2796203.16 8749965921.6113142872 4042278348 4044389824 1613032969

208 65537.928513.1 8558466369.2 3877647873.2131 6654212673.71566847 0267111297

209 3.419.683.174763.34 1062328465 4639440707.1 6077920187 8039402409 5514317003

210 5.5.13.29.41.61.113.421.1321.1429.14449.7416361.47392381.14 6919792181.

.104181 5865690181 210

211 3.4643.9878177.5344743097.19 9061567251.22 4811275125 7517586423 4185190299

212 17.1692645313.109 2051360401 8498900801.20 9460015914 2901219928 1424246257

213 3.3.5113.17467.102241.56409643.1395 2598148481.2035255457 6630130693 3226271929

214 5.857.843589.817 4912477117.2352 8569104401.378668090 6166005726 4219253397

215 3.11.9084611.293 2031007403.5990 4608378705 6613774301 8260871169 8924130721

216 97.257.577.673.209924353.4261383649.48 7824887233.249290 6081826536 0451708193

217 3.43.16233337.715827883.14050860 8590164280 2259342330 9886684274 5808905947

218 5.5669.666184021.7432 3515777853.174651885 2140345553.1 7185764601 2809566969

219 3.3.1753.907019 7542196643.179591803 8741070627.32782446 9015622243 4135906137

220 17.353.61681.109121.148721.2931542417.3404676001.1103 5465708081.

.254671 7317681681 220

221 3.443.2731.43691.471 4692062809.450 7513575406 4465158454 0145836674 1487526913

222 5.13.149.593.3109.184481113.231769777.1398316729.4345052821.

.14 5303029800 1690873541 222

223 3.21 9256122131.204934 9592090504 3950407650 4509181712 6031830315 4708405513

224 641.6700417.1677 7388527684 9215533569.37414 0571613223 7595740814 8834323969

225 3.3.3.11.19.251.331.4051.18837001.4714696801.113 3836730401.

.2819414 7295371017 7758647201 225

226 5.58309.2362153.150 7911621390 1326178369.10384 5937170696 5511294580 4582584321

227 3.297371.345463157 9714210387.6998 2170658265 4447131175 4525871203 1103399659

228 17.241.1217.90289.148961.9036489073.2451 7014940753.

.290340571 6492099337 9000074993 228

229 3.18754643.15 3334171410 0379433916 4342447265 4261588519 4618245196 3484372297

230 5.5.41.277.461.1013.1657.5981.30269.15096281.1021622741.7834788541.

.3 5900691276 5190408181 230

231 3.3.43.67.617.683.5419.14323.20857.78233.3 5532364099.

.70 1807961652 7704034924 5703851057 231

232 257.929.5569.8353.39594977.1569460400 6012505869 8512211693 6559405063 7743819041

233 3.467.27961.352 3693740136 6013947257 4531568890 6781550405 6300762074 2839120913

234 5.13.13.37.53.109.157.313.1249.1613.3121.7489.21061.21841.348661.

.111 2388285061.37024440 5487013669 234

235 3.11.283.16 5768537521.32 8006342451.46179790 7949997211.

.2354573 7451009211 5086834691 235

236 17.1889.11329.84961.765373489.466781343 9458532797 3927972315 1768042279 5032583489

237 3.3.647011.13664473.2014 8763660243 8195784363.

.13775 6946928984 9218474470 9216599873 237

238 5.29.113.137.953.2381.9521.26317.42841.823481.53629 6539263941.

.182928 9898415691 6156396101 238

239 3.340337.326051 4298370422 1670173899.2 6537037220 9921127851 7485616123 9437662001

240 193.23041.65537.414721.22253377.4447 9210368001.

.14768 7843070090 6164431823 6958041601 240

xxix Prime Factors Short 2+

241 3.2411.1 0411181203.1505982 8108442641.

.311 5949925222 9005146647 3694174624 8477210667 241

242 5.397.2113.3389.91961.40369 6258401080 7014809213.

.1339 2725398336 6838695892 0468400193 242

243 3.3.3.3.3.3.19.163.1459.87211.135433.139483.272010961.

.1042940743 1911334611.9 1812505160 2568899753 243

244 17.977.3 7831175201.48 8994002930 9876547089.9200725 8710786975 0007279622 7876997617

245 3.11.43.281.491.86171.436 3953127297.1516286875 8218274451.

.506472820 3579612588 5000330641 245

246 5.13.2953.10169.181549.12112549.43249589.802333429.602704 3735173469.

.1 2596597697 6392564317 246

247 3.2731.174763.207481.10049443.355011619.

.21337 9941663827 5927018195 5810236817 0760508803 247

248 257.8929.197107422 2730143019 1978141446 6039325387 8896236763 4270585075 2210599969

249 3.3.499.1163.2657.155377.1 3455809771.920 2419446683.

.3388098 2905675873 7705201652 5627948593 249

250 5.5.5.5.41.101.7001.8101.28001.96001.268501.3775501.

.4797013360 3445383501.9429186693 2171243501 250

251 3.238451.5058345723 9518546885 0566542884 6313806490 9031216773 6435890119 9128608233

252 17.241.433.1009.3361.21169.38737.2627857.15790321.269389009.8 8959882481.

.14 7520467919 0128571777 252

253 3.683.4049.85009.2796203.31797547.8 1776791273.

.2822551529 4603308476 0426208614 9015242689 253

254 5.509.18797.26417.72118729.140385293.279 2688414613.898 8357880501.

.901 3356691791 3517709497 254

255 3.3.11.307.331.2857.6529.12241.43691.41856 2986357561.

.2683142303 6065352611.5136614945 5494753931 255

256 123892 6361552897.93 4616397153 5797776916 3558199606 8965840512 3754163818 8580280321

257 3.3723 9639534523.5 1814415660 2508243009.

.400 0659204579 1147533123 1087884704 3394855313 257

258 5.13.173.17029.46957.101653.500177.175 9217765581.9675877 1543686753.

.59516 3196629668 5834686149 258

259 3.43.1777.25781083.1 4562355969 0431904173 8812533139.

.107636 3442178404 1313919350 0838915409 259

260 17.42641.61681.858001.5746001.308761441.2400573761.6 5427463921.

.1733083 4391887481 0521923841 260

261 3.3.3.19.59.523.3033169.6929826139.9607679 1871613611.

.345341290 1832690553.3356385645 0515702761 261

262 5.269665073.642811237.2745098189.81 0791440841.1245075181 5271172041.

.3 0854469540 9769427309 262

263 3.1579.92051.2926111 4397558193.

.11616 2540620454 0347970098 0637033639 4690273608 6742697099 263

264 97.257.673.229153.119782433.4 3872038849.1687508 1675650881.

.86 9453889972 1044282825 9494992321 264

265 3.11.107.2805 9810762433.5937 8367896686 3030035641.

.1007715965 8757482267 4547298968 7556259131 265

266 5.29.113.229.457.1597.2129.525313.12684 8469231149.67925 3585011429.

.4493293862 9223253525 0647435097 266

267 3.3.179.3739.4273.62020897.1858477 4046020617.

.799336 4465170792 9987163376 9103325135 0895453313 267

268 17.75041.33380 8138537249.

.1 1137670944 2219990060 5896348724 7870451619 9747868775 1948513969 268

269 3.4242 5591579618 7428893811.

.7452803 5219178635 8209397071 7083291982 8505783238 4965565161 269

270 5.5.13.37.41.61.109.181.541.1321.30241.49681.54001.246241.279073.29247661.

.16504 1853060421.16624293 5471754241 270

Short 2+ Prime Factors xxx

271 3.1627.11541796 6565804897.46 3526001587 3357770993.

.1453023029 4820448549 4451955596 4740294049 271

272 5441.65537.335631 8270467982 4541060373 0138717057.

.63406006 4077277210 4210983422 0642811713 272

273 3.3.43.547.2731.5419.224771.1210483.22366891.2 5829691707.10 5310750819.

.2926531131 4715720577 9127526827 273

274 5.189061.16843 4085820849.2068756 7010495774 4917147613.

.921525 7079118405 8739061733 0886362701 274

275 3.11.11.251.683.2971.4051.48912491.

.1 6571548087 5502181882 0630633083 4006188611 3557440895 5395309601 275

276 17.241.57 7033894648 1798744593.2912800 0924361888 8211558641.

.17 6319698878 6001415857 4508770817 276

277 3.2579 2643401363.

.3138280009 3996790173 4463105154 2622769205 8771349538 4512820233 4345822857 277

278 5.557.1408349.1 5736774913.49 2717674609.1276 3660054721.

.1251163891 2999676358 6027250922 9764287909 278

279 3.3.3.19.26227.529510939.715827883.2903110321.11 9232435043.

.8538 4915399027.64443 6537614061 1199022187 279

280 257.4481.5153.557761.736961.4278255361.5 4410972897.

.342 1249381705 3680398303 3419004621 1225116161 280

281 3.563.5203536083.

.44 2079688503 1728601766 0721775242 4068059658 8646159653 4138464710 7224486419 281

282 5.13.1129.3761.5641.1768141.54865357.7484047069.18 0846660913.

.14073 7471578113.2700 9726848416 7653999069 282

283 3.1699.62827.2486265371.6753 5788803713.

.2890 3228675505 1820954283 5620713954 0470183011 5983581457 283

284 17.2273.1433633.P75

285 3.3.11.331.571.2281.174763.1101811.160465489.301134747 9614249131.

.15653990 7058963135 4726923722 0041169361 285

286 5.53.157.397.1613.2113.25741.958673.3426853.9467173.417016557 0896115649.

.6615213493 5110533966 8937661297 286

287 3.43.83.1723.8831418697.8441323 8703660609.433679083 1080504259.

.4169 1369467730 0071327079 0657459827 287

288 641.3457.816769.6700417.1844674406 9414584321.15 6298590135 0085709953.

.14223467 3897585364 4793916289 288

289 3.43691.72251.79187.1077971.1836 0250452977.19776680 3208315851.

.338858 7330655984 0135519553 9629373089 289

290 5.5.41.17401.168781.107367629.536903681.24 4716883381.390209519 2430070721.

.120045415 0195481108 5302214141 290

291 3.3.971.1553.25609.31817.563696 3037465601.58154660 6903256979.

.110087601 8364883721.9969550342 7255026561 291

292 17.1960288071 0043505617.

.23877558 3705851535 3525512526 7231814835 9938430791 8588310703 4076803873 292

293 3.587.26371.33403.13453 8907795406 3294533189 2129844577.

.76 2551893101 4101660193 9028304752 0363896913 293

294 5.13.29.113.197.1429.14449.540961.1 9707683773.498 1857697937.

.4054485969 3521152369.170594 1050473832 3992180849 294

295 3.11.2833.37171.1824726041.

.1 0038903777 1499109461 2674101710 8754570611 9421915605 9132543172 8188591011 295

296 257.80513.P82

297 3.3.3.3.19.67.683.5347.20857.23761.87211.694387.621 5074747201.

.24209 9935645987.14 9738668971 7526522806 3698945547 297

298 5.1789.1 2961064789.1464 1916303149.272433866 0239558843 7243602121.

.11011 8089519717 4591531324 2336927641 298

299 3.2393.2731.2796203.83449 0119087067.

.22 2634853434 3568341269 3923533443 9170326131 5794314607 7977190561 299

xxxi Prime Factors Short 2+

300 17.241.401.61681.340801.2787601.3173389601.4562284561.

.146150303 1127477825 0999793695 4347312254 8042956801 300

301 3.43.43.293 2031007403.P75

302 5.43 7368927017 6379261201.1305 3032390189 9210670077.

.285449 5385411919 7621164963 8103526435 8442074113 302

303 3.3.112102729.8451004001 5215293433 1135470251.

.191 1268421495 7755703306 2902193401 4085981307 2336321619 303

304 65537.7798338113.17 9781388993.8488 5296460737.64396 6863870017.

.2736225 4540091201.2 3715782724 3967596481 304

305 3.11.331841.76861433 6404564651.3134755923 2075126851.

.24705433 6699552168 8879618002 9292171557 1154497761 305

306 5.13.37.109.137.409.613.953.3061.13669.26317.2582029.4260133.318194713.

.1326700741.1245872 3489217613.23849519 7879143209 306

307 3.1249678499.431 5199443523.2 1070882506 3558235331.

.7649015092 3395684178 4724040034 0186028665 5314439889 307

308 17.353.13553.15790321.2931542417.7 4153335873.

.18679350 2331732804 8519811865 5253377126 5353820673 7478396129 308

309 3.3.619.2473.15451.89620507.41 5141630193.240 0744384937.9827 7023988499.

.6854585 2036177507.814276708 1771726171 309

310 5.5.41.5581.8681.37201.49477.87421.384773.52597081.8973817381.

.2486589969 3834809641.578058 2874569275 8010628581 310

311 3.64067.P89

312 97.257.673.4993.94849.789198817 2627109114 3763623681.

.1330632041 8205909319 9406053090 1902403470 3545187073 312

313 3.P94

314 5.2790467761.594103 5366826969.22 0394203343 9148343973.

.18268770 4666362864 7754612085 5244518477 1578920961 314

315 3.3.3.11.19.43.211.281.331.5419.86171.664441.1564921.1765891.18837001.

.7 7158673929.11247702 5996765054 8144713799 1664348691 315

316 17.504337.994769.P83

317 3.326330579.49198112 2308467411.

.554346309 1988411897 3820024772 5749800421 1566855787 0254543923 0498849139 317

318 5.13.10177.207973.15358129.586477649.180143 9824104653.

.300074 5925439318 1618012897.79718620 0486710330 3293462593 318

319 3.59.683.3033169.12 1333341977.16952351 4238420211.

.259255 1649443838 2632167017.5 4618593734 9808777105 3790065009 319

320 274177.286721.446960641.9 6645260801.6728 0421310721.344240405 1886487041.

.2715 8620059314 0659941957 5483412481 320

321 3.3.643.154723.2 0636399209.4806 2571001539 4052365153.

.57187 6196978869 7451457489.841157474 4904788148 8635567801 321

322 5.29.113.277.1013.1657.1933.3221.30269.169373.298817.209160253.

.11 5927640417.1 7935157473 6387915177.270 3702811844 8801270021 322

323 3.43691.174763.1779583090 8608814443.32 1158605463 9813621611.

.63 1995764203 3539607139.20652 5587851947 5622261353 323

324 17.241.433.1297.3889.38737.30433969.33975937.1164777409.371 8266498433.

.13492 1168163073.13899 1501037953.117402 9487714513 324

325 3.11.131.251.2731.3251.4051.409891.5840251.7623851.781 2610577851.

.986094 2209386451.1245 6609072141 6978192656 1543788801 325

326 5.653.9781.7807049.4826612561.97161 3420158567 9932947173.

.1169201309 8647223345 6294834974 3354261576 4159168513 326

327 3.3.666427.104124649.6927735019.20777 5684736234 8863128179.

.3041402847 0765822165 9765815081 6186643260 2988327347 327

328 257.1223 9719573537.1809392703 9368350337.2539452441 5842506913.

.37832 1539354637 5954710134 8940698390 3120592833 328

329 3.43.283.659.16 5768537521.76239 4321774681.

.359687 4243779617 1475089176 3743933975 3349592001 0375948584 0227631801 329

Short 2+ Prime Factors xxxii

330 5.5.13.41.61.397.661.1321.2113.3301.8581.312709.4327489.39 1249826881.

.41 5878438361.363 0105520141.1212 7627350301.1337 9250952981 330

331 3.5297.2983001129.7520796641.85306742 5084227471 7434530683.

.143839019 9144030563 3648068637 0451018942 9516419097 331

332 17.11953.1476 7689550320 1728087421 7482806234 7720350769.

.29 1554779734 3721112173 4464826285 2905777597 9692132113 332

333 3.3.3.19.1777.3331.17539.304363.25781083.985 3387597819.10777 5231312019.

.3103132 0083857011.1 2705931446 4650523301 3326197403 333

334 5.75005713.2739532 5377910797.182082 6078119015 6536114609.

.1 8707220957 8355573530 0716392448 7111268189 2570202113 334

335 3.11.93131.7327657.671 3103182899.P75

336 193.449.2689.65537.22253377.47886721.183076097.35842 9848460993.

.1 3108430448 5119425504 2844951198 8952999601 9181850241 336

337 3.21569.5333388961.96409 4242760707.

.84 1462035388 4002547092 0013080114 0475354660 3219833407 0924679705 8685767257 337

338 5.53.157.677.1613.180201997.125 9036730797.61594 6323850313.

.4089468 7672970399 2293841657.2156563293 8289155092 0192462661 338

339 3.3.227.48817.156619.28448881.636190001.49100336 9344660409.

.80676 7008285880 2084066104 0633174106 3631088159 0473931569 339

340 17.17.1361.61681.354689.12717361.139 2971637361.287 9347902817.

.80 8822074662 7020943841.630 8949053951 4352822182 6310327361 340

341 3.683.647219.1434929.715827883.3736 8615235403.

.88001 3382343267 0069531598 6455482272 5863557823 1014418804 7003818403 341

342 5.13.37.109.229.457.25309.131101.160969.525313.4598533.5675149.39291697.

.27 5415303169.9946 3730244517.414356 0637122783 5355919073 342

343 3.43.2513690593.436 3953127297.288358003 0222424891.

.4 3911158594 9501945221 0297067047 1807966748 6165417704 8737558611 343

344 257.4129.P98

345 3.3.11.139.331.691.2796203.1884103651.16 8749965921.34576 7385170491.

.740 7834313249 9989110265 4092506180 4532326371 5522281571 345

346 5.1 3625405957.715 2893721041.1673815085 1865747003 2217423206 9942181681.

.17 5739665310 5057529688 7774035031 3227534889 346

347 3.P104

348 17.241.59393.82129.1038947 6529713761.593 7202117116 4475019217.

.5652 8819562467 8452623377.822801951 6714411983 2390568177 348

349 3.131282633.P97

350 5.5.5.29.41.101.113.701.8101.268501.7416361.47392381.

.2430 0659246935 1719855032 2751963101.1038213 7934478419 4090829335 5871461401 350

351 3.3.3.3.19.2731.87211.22366891.53 0230622637 0307681801.

.42477 1330322455 2237738169.2 4841125429 0515850625 3896175126 9988364169 351

352 641.1409.1258753.6700417.4 4199554137 8330835457.

.2724766 0046495954 3415724134 3741767729 1568912064 2291857021 1139111809 352

353 3.3803909 5720787468 3729509405 1706948091.

.1607818533 3844857077 0784283714 6335251451 1620177625 1955702995 5613946641 353

354 5.13.709.1181.3541.12037.31153.157649.174877.5397793.5521693.94789873.

.10 4399276341.2084785 8316750657.29952400 8711790907 8735942093 354

355 3.11.56409643.1395 2598148481.1552463 5883992211.

.182013944 0299162539 8485059929 0949064721 0895874589 0680991855 2581277361 355

356 17.P106

357 3.3.43.307.2857.5419.6529.43691.428401.823679683.1 4316255316 5560959297.

.110 7523122161 8592513745 7604662074 3436324958 8723425331 357

358 5.31815461.1301260549.4 1611501383 0990336221.115757 0933663659 5278866333.

.58885 0381287433 0282790841 1047440018 1861465037 358

359 3.3536450843.111067 1633637523.1 9419397456 3158088483.

.513 1663047139 9975121756 0795536588 3672489250 4352778204 2775106649 359

xxxiii Prime Factors Short 2+

360 97.257.577.673.8369281.394783681.4278255361.4 6908728641.48 7824887233.

.7 5001689028 3777055704 7382272474 7448536633 8380663681 360

361 3.174763.687 4301617534 8275093505 7576845435 6245025403.

.1 3032541164 6110869726 8759335821 5858608970 0841594672 0083246259 361

362 5.9413.2873 9737348957.17892 5762979037.383053 8323149121.

.9501637613 5553173181.10 6646454159 1577895336 8533937767 9881781493 362

363 3.3.67.683.2179.20857.117371.1948 8182484739.110541845 8279780045 5736061107.

.3969926664 5852731908 2713961772 9892812435 5765422009 363

364 17.858001.15790321.308761441.59391 4915675537.

.88 9699724270 9548683826 3404334155 5740249741 9842475785 1044517845 1442481793 364

365 3.11.1753.581874971.179591803 8741070627.498 3860557465 3477927323 1850742131.

.249442 5222574733 2143392783 9695094696 7011483971 365

366 5.13.733.1709.3456749.5080081.36 8140581013.66 7055378149.420 9508589941.

.1283 6737570021.1912555 6519918081.4141 9495873379 6530899181 366

367 3.2203.19819.14626 4881313513.2083706288 5084633147.

.460 2336168618 5206616518 0033789571.1636198 5971696072 4508833163 3873083979 367

368 65537.7639 2570609857.1335 5703465746 3136395439 0476479681.

.899153739 3792277787 7614505795 5765742805 6187413080 2566460033 368

369 3.3.3.19.83.739.18451.165313.174907.8831418697.2630 9368807003.

.1319431 7913029593.2336504108 3799063007 2450102924 0892793000 7906086731 369

370 5.5.41.149.593.29246281.184481113.231769777.567471221.1392776941.

.496416 6554103541.125871072 5115650761.42998818 3417207835 0686174001 370

371 3.43.107.2805 9810762433.1835194 5672220987.104718 4633680244 0580575859.

.903389 0180249079 3533882683.7153028 9557450198 7260955609 371

372 17.241.1489.29761.290657.3770202641.2241539 8357688737.

.11 4162918040 1976895873.188944042 5670100451 9961801954 4265113096 6948029537 372

373 3.60427.69457949 7316894264 4256612436 5980637197 2188318857.

.1527967563 2529004346 2779779478 7583287059 0594752132 7614399129 373

374 5.137.397.953.2113.5237.26317.551353793.2 6509131221.181 9762572673.

.3515507 7044989397.40 2929206562 9191839853.1353 2204591711 8601273437 374

375 3.3.11.251.331.2251.4051.229668251.113 3836730401.55 1948541833 6288303251.

.199 6377842904 6466946251.35758 6331315969 0068505137 8954141001 375

376 257.3308801.3853249.4 8707339993 9357470433.1638 7553063670 2837695009.

.26739 8978418337 8728255297.2200793305 8914598980 7908723201 376

377 3.59.2731.3033169.13454377.P95

378 5.13.29.37.109.113.757.1429.14449.246241.279073.4 0388473189.11 8750098349.

.4563764310 5362633947 3533320957.304 8327561958 6522928480 7891468769 378

379 3.1501 2732261073.7280409237 2182169758 6308784409.

.3 7551870149 1602259335 1084199842 5767070380 4455424672 1900967363 8189257459 379

380 17.1217.61681.148961.2451 7014940753.3435950 2103163357 2415775800 0789490561.

.1 5378727933 0237476887 1063312332 3952575663 5010497681 380

381 3.3.3049.3825718 4231365987.56713727 8201564105 7722910123 8628035243.

.827231 7928370755 8079607521 7983125217 7118476669 7594996913 381

382 5.3821.25212001.5972216269.8961 8875387061.

.1833085153 8426654426 5228323416 5143433597.

.2 0844252715 3792520909 3848500344 7004944677 382

383 3.13517 1073178598 1752792617.56091 2281791431 3723820539.

.866140 5537430414 7785922588 7851118773 8680452563 3977953656 3782349481 383

384 5964958 9127497217.57 0468920068 5129054721.3496218393 2692179569 4385454593.

.33119238 0488114152 6004574284 9795340851 2758882817 384

385 3.11.11.43.281.617.683.2971.78233.86171.48912491.219980531.3 5532364099.

.4 3629892114 2286134032 0935785851.1276 1303086455 0082934161 4664372811 385

386 5.773.3089.148997.1440203064 4704405877.6 3528368960 3233836449.

.3787913000 2708963567 7652285973.25564 7743603632 1274038224 7547878573 386

Short 2+ Prime Factors xxxiv

387 3.3.3.19.1033.1591582393.293 2031007403.1568 6603697451.

.1090536789 6894030236 4939183451.

.7451156 8294243628 8633065028 2569882523 9868474219 387

388 17.25507121.P109

389 3.107 4456464321.136937 9108017267.274209 4407638203.P75

390 5.5.13.13.41.53.61.157.313.521.1249.1321.1613.2341.3121.21841.51481.

.468781.34110701.723447661.10814 0989558681.

.892527 8993793241.7204 5377242751 8446437641 390

391 3.2347.43691.1578859.2796203.194902553.29143833 4156037699.

.2911194824 8642861801.22 4571405277 1430777876 1430067868 3897932954 9117936841 391

392 257.3137.5153.50177.101921.258721.5 4410972897.P83

393 3.3.787.1049.4744297.1823311286 8120778178 4391813611.

.7237 4970654455 4305500305 7643920459.

.43 3685074806 8862980289 1926711765 5888254843 393

394 5.4729.52009.1079423677.15 2874915601.51480 3697091705 0130439411 8553664009.

.38621 6338580579 8697201354 7951946615 1272644136 4448411929 394

395 3.11.5531.1415681.2014 8763660243 8195784363.P85

396 17.241.353.433.7393.38737.1761345169.2931542417.9 8618273953.31 1712063697.

.5 6695862294 8012073585 6356719714 1118195727 7548591444 4634179633 396

397 3.13499.321571.476401.17414009.P97

398 5.797.7655 4648784441.209907 3106303095 0253038854 6087971791 8033130293.

.10081167 1534441046 1444141839 6101802392 2317850375 1442552629 398

399 3.3.43.571.4523.5419.63841.174763.160465489.113556903 2520567138 0495907537.

.1067882904 4384829528 4382097033.109 8012961987 4039209485 8844294643 399

400 65537.414721.4447 9210368001.339942637 7632056001.48504 8422208437 1979240001.

.1295 4118820893 5646963818 8447165919 8620897441 0651257601 400

Short 10􀀀

Factorizations of 10n 􀀀 1, n _ 150

n Prime Factors

1 3.3

2 3.3.11

3 3.3.3.37

4 3.3.11.101

5 3.3.41.271

6 3.3.3.7.11.13.37

7 3.3.239.4649

8 3.3.11.73.101.137

9 3.3.3.3.37.333667

10 3.3.11.41.271.9091

11 3.3.21649.513239

12 3.3.3.7.11.13.37.101.9901

13 3.3.53.79.265371653

14 3.3.11.239.4649.909091

15 3.3.3.31.37.41.271.2906161

16 3.3.11.17.73.101.137.5882353

17 3.3.2071723.5363222357

18 3.3.3.3.7.11.13.19.37.52579.333667

19 3.3.111111111 1111111111

20 3.3.11.41.101.271.3541.9091.27961

21 3.3.3.37.43.239.1933.4649.10838689

22 3.3.11.11.23.4093.8779.21649.513239

23 3.3.111 1111111111 1111111111

24 3.3.3.7.11.13.37.73.101.137.9901.99990001

25 3.3.41.271.21401.25601.18 2521213001

26 3.3.11.53.79.859.265371653.1058313049

27 3.3.3.3.3.37.757.333667.44033 4654777631

28 3.3.11.29.101.239.281.4649.909091.121499449

29 3.3.3191.16763.43037.62003.7 7843839397

30 3.3.3.7.11.13.31.37.41.211.241.271.2161.9091.2906161

31 3.3.2791.6943319.5733641506 3790604359

32 3.3.11.17.73.101.137.353.449.641.1409.69857.5882353

33 3.3.3.37.67.21649.513239.134462821 0313298373

34 3.3.11.103.4013.2071723.5363222357.2 1993833369

35 3.3.41.71.239.271.4649.123551.10259880 0232111471

36 3.3.3.3.7.11.13.19.37.101.9901.52579.333667.99 9999000001

37 3.3.2028119.247629013.22 1239429677 0203368013

38 3.3.11.90909090 9090909091.111111111 1111111111

39 3.3.3.37.53.79.265371653.9009 0090090099 0990990991

40 3.3.11.41.73.101.137.271.3541.9091.27961.1676321.5964848081

41 3.3.83.1231.538987.2017637099 0032280374 8657942361

42 3.3.3.7.7.11.13.37.43.127.239.1933.2689.4649.459691.909091.10838689

43 3.3.173.1527791.196350 6722254397.214099201 5395526641

44 3.3.11.11.23.89.101.4093.8779.21649.513239.1052788969.1056689261

xxxv

Short 10􀀀 Prime Factors xxxvi

45 3.3.3.3.31.37.41.271.238681.333667.2906161.418550283 0133110721

46 3.3.11.47.139.2531.54979 7184491917.111 1111111111 1111111111

47 3.3.35121409.316362908 7634585250 0140615403 8726382279

48 3.3.3.7.11.13.17.37.73.101.137.9901.5882353.99990001.999999 9900000001

49 3.3.239.4649.505885997.1976 7301445981 9096356802 3014679333

50 3.3.11.41.251.271.5051.9091.21401.25601.18 2521213001.7887 5943472201

51 3.3.3.37.613.210631.2071723.52986961.5363222357.1316816 4561429877

52 3.3.11.53.79.101.521.859.265371653.1058313049.19 0038197677 7332243781

53 3.3.107.1659431.132581526 7337711173.471988 5879949142 5660200071

54 3.3.3.3.3.7.11.13.19.37.757.52579.333667.70541929.1 4175966169.44033 4654777631

55 3.3.41.271.1321.21649.62921.513239.83251631.13006 3569267805 8358830121

56 3.3.11.29.73.101.137.239.281.4649.7841.909091.121499449.1 2752200102 0150503761

57 3.3.3.37.21319.10749631.111111111 1111111111.39311 2302230512 9377976519

58 3.3.11.59.3191.16763.43037.62003.7 7843839397.1540832 0493066255 7781201849

59 3.3.255 9647034361.434087 6285657460 2121445342 8992855982 6755746751

60 3.3.3.7.11.13.31.37.41.61.101.211.241.271.2161.3541.9091.9901.27961.

.2906161.4188901.39526741 60

61 3.3.733.4637.329401.974293.1360682471.10600 7173861643.706170999 0156159479

62 3.3.11.2791.6943319.5733641506 3790604359.9090909090 9090909090 9090909091

63 3.3.3.3.37.43.239.1933.4649.10837.23311.45613.333667.10838689.45121231.

.192143 6048294281 63

64 3.3.11.17.73.101.137.353.449.641.1409.19841.69857.976193.5882353.6187457.

.83442 7406578561 64

65 3.3.41.53.79.271.265371653.16 2503518711.5538396 9973640240 5628651064 0780600481

66 3.3.3.7.11.11.13.23.37.67.4093.8779.21649.513239.599144041.18 3411838171.

.134462821 0313298373 66

67 3.3.493121.7986359577 8924342083.2 8213380943 1766670012 6315366099 9177245677

68 3.3.11.101.103.4013.2071723.28559389.1491383821.5363222357.2 1993833369.

.232455 7465671829 68

69 3.3.3.37.277.20386 4078068831.111 1111111111 1111111111.

.15953520 8632922464 4348978893 69

70 3.3.11.41.71.239.271.4649.9091.123551.909091.4147571.10259880 0232111471.

.26521279 3249617641 70

71 3.3.2415731423 9362767357 6957439049.4 5994811347 8868463102 2172889522 3034301839

72 3.3.3.3.7.11.13.19.37.73.101.137.3169.9901.52579.98641.333667.99990001.

.99 9999000001.319904 4596370769 72

73 3.3.1 2171337159.185519384 2151350117.

.4920 7341634646 3269340017 3948250213 1487446637 73

74 3.3.11.7253.2028119.247629013.42265 0073734453.29655734 7313446299.

.22 1239429677 0203368013 74

75 3.3.3.31.37.41.151.271.4201.21401.25601.2906161.18 2521213001.

.15763 9855537391 9170916417 0940063151 75

76 3.3.11.101.72281703 6322379041.90909090 9090909091.111111111 1111111111.

.136977818 7490592461 76

77 3.3.239.4649.5237.21649.42043.513239.29920507.

.13661 4668576002 3293714964 4755591574 0910181043 77

78 3.3.3.7.11.13.13.37.53.79.157.859.6397.216451.265371653.1058313049.

.38 8847808493.9009 0090090099 0990990991 78

79 3.3.317.6163.10271.307627.4917219553 6083790769.

.366 0574762725 5214615271 4056487508 0461079917 79

80 3.3.11.17.41.73.101.137.271.3541.9091.27961.1676321.5070721.5882353.

.5964848081.197210 6116664671 7498359681 80

81 3.3.3.3.3.3.37.163.757.9397.333667.2462401.44033 4654777631.

.67642 1558270641.1306548 9780800777 8425046117 81

xxxvii Prime Factors Short 10􀀀

82 3.3.11.83.1231.538987.267050278 1396266997.34 0419382980 6058997303.

.2017637099 0032280374 8657942361 82

83 3.3.336 7147378267.95125385 0862415437 3682136329.

.34 6895716385 8578045447 4113739450 5425384477 83

84 3.3.3.7.7.11.13.29.37.43.101.127.239.281.1933.2689.4649.9901.226549.

.459691.909091.10838689.121499449.445819222 3320340849 84

85 3.3.41.271.2071723.262533041.5363222357.811 9594779271.

.422 2100119405 5301701793 3119029148 8789678081 85

86 3.3.11.173.1527791.57009401.2182600451.196350 6722254397.

.214099201 5395526641.73061 1655657181 7748755241 86

87 3.3.3.37.3191.4003.16763.43037.62003.72559.7 7843839397.

.31017025 1658029759 0451577932 3733949834 2763245483 87

88 3.3.11.11.23.73.89.101.137.617.4093.8779.21649.513239.1052788969.

.1056689261.16205834 8460129675 8492708265 6402106953 88

89 3.3.497867.103733951.10 4984505733.50785 5496602631 5671444089.

.403513310 2228090532 8493281847 5878953159 89

90 3.3.3.3.7.11.13.19.31.37.41.211.241.271.2161.9091.29611.52579.238681.

.333667.2906161.3762091.898 5695684401.418550283 0133110721 90

91 3.3.53.79.239.547.4649.14197.17837.4262077.265371653.4 3442141653.

.31687736 5766624209.1107421 8647053005 4291318013 91

92 3.3.11.47.101.139.1289.2531.1837 1524594609.54979 7184491917.

.111 1111111111 1111111111.41810033 0007166986 7932658901 92

93 3.3.3.37.2791.6943319.5733641506 3790604359.

.9009009009 0090090090 0900900900 9909909909 9099099099 0990990991 93

94 3.3.11.6299.35121409.485506 7598095567.2972627 0500913900 6771611927.

.316362908 7634585250 0140615403 8726382279 94

95 3.3.41.191.271.59281.63841.111111111 1111111111.

.12899812 3195084954 3985493631.965 1946171216 4079145607 0347951751 95

96 3.3.3.7.11.13.17.37.73.97.101.137.353.449.641.1409.9901.69857.206209.

.5882353.99990001.6 6554101249.7511 8313082913.999999 9900000001 96

97 3.3.12004721.846035 7313969192 3376721153 7899097169.

.1093 9984685537 0537540339 2668420701 1910766229 6580348039 97

98 3.3.11.197.239.4649.909091.505885997.1976 7301445981 9096356802 3014679333.

.5076141624 3655329949 1878172639 5939035533 98

99 3.3.3.3.37.67.199.397.21649.34849.333667.513239.134462821 0313298373.

.3 6285372434 2990469324 7662354742 6886978631 1886053883 99

100 3.3.11.41.101.251.271.3541.5051.9091.21401.25601.27961.60101.7019801.

.18 2521213001.1410 3673319201.7887 5943472201.168058 8011350901 100

101 3.3.45315301 8181661323 4555190841.129 0632822328 4896195198 5354966759.

.1 8998088572 8193752528 4207842137 4368604969 101

102 3.3.3.7.11.13.37.103.613.4013.210631.2071723.52986961.5363222357.

.2 1993833369.29 1078844423.1316816 4561429877.3 7752695530 9799110357 102

103 3.3.1031.7034077.P93

104 3.3.11.53.73.79.101.137.521.859.1580801.265371653.1058313049.

.19 0038197677 7332243781.63 2527440202 1507450906 2241224544 3923049201 104

105 3.3.3.31.37.41.43.71.239.271.1933.4649.123551.2906161.10838689.

.3 0703738801.62 5437743071.10259880 0232111471.578020 5030878619 1965409441 105

106 3.3.11.107.1659431.132581526 7337711173.471988 5879949142 5660200071.

.90 9090909090 9090909090 9090909090 9090909090 9090909091 106

107 3.3.643.999809.9885089.215257037.2386760191.51139953 8427507881.

.64682695 0155548399.10288079 4672225387 9130231155 6310051849 107

108 3.3.3.3.3.7.11.13.19.37.101.109.757.9901.52579.153469.333667.70541929.

.1 4175966169.99 9999000001.44033 4654777631.597795771 5633453386 6654838281 108

109 3.3.1192679.7 1276748097 1213008079.52 9527534876 7234696493.

.2468297439 8435543596 2408390910 3782185372 8210515008 6881669547 109

110 3.3.11.11.23.41.271.331.1321.4093.5171.8779.9091.21649.62921.513239.

.83251631.2 0163494891.3187 2784116567 4579776721.13006 3569267805 8358830121 110

Short 10􀀀 Prime Factors xxxviii

111 3.3.3.37.37.2028119.247629013.3055705 1518647307.22 1239429677 0203368013.

.88459 8117086562 9119271997.900778143 9605501793 8257237117 111

112 3.3.11.17.29.73.101.113.137.239.281.4649.7841.909091.5882353.121499449.

.7376575589 6403138401.1 2752200102 0150503761.1199683 6914484637 0226083377 112

113 3.3.227.90 8191467191.P98

114 3.3.3.7.11.13.37.21319.1458973.10749631.90909090 9090909091.111111111 1111111111.

.39311 2302230512 9377976519.7532018062 7132846254 7977919407 114

115 3.3.41.271.31511.1 9707665921.2041413 7203567631.111 1111111111 1111111111.

.57999515 1394138214 4830754391.1224035694 9178366272 0773144041 115

116 3.3.11.59.101.349.3191.16763.38861.43037.62003.618049.7 7843839397.

.1540832 0493066255 7781201849.1181 1806375201 8364086796 3573625866 9583187541 116

117 3.3.3.3.37.53.79.333667.265371653.24039 6841140769.53794 7698126879.

.335282 5314499987.9009 0090090099 0990990991.23040173 8448408513 1816292573 117

118 3.3.11.1889.255 9647034361.10 9080584206 8098677837.

.4411 9227709960 7410964453 5362851087.

.434087 6285657460 2121445342 8992855982 6755746751 118

119 3.3.239.4649.923441.2071723.5363222357.392 4966376871.

.7687365594 2140124904 2753476963.

.32301294 2148562751 6508145444 3735045464 0448842187 119

120 3.3.3.7.11.13.31.37.41.61.73.101.137.211.241.271.2161.3541.9091.9901.

.27961.1676321.2906161.4188901.39526741.99990001.5964848081.

.100 0099999998 9998999900 0000010001 120

121 3.3.15973.21649.38237.274187.513239.P96

122 3.3.11.733.4637.81131.329401.974293.1360682471.10600 7173861643.

.706170999 0156159479.

.112052 2253011683 6855321528 2578904375 7514502359 2596037161 122

123 3.3.3.37.83.1231.538987.1811791.62 6920594693.942585697 6319889649.

.2017637099 0032280374 8657942361.

.841 4640003465 1612031199 7890655805 4839526493 123

124 3.3.11.101.2791.2049349.6943319.5733641506 3790604359.

.9090909090 9090909090 9090909091.

.4831 2854955451 2237305554 5883590398 2239730714 9685578249 124

125 3.3.41.271.751.21401.25601.1797655751.18 2521213001.17614 4543406001.P74

126 3.3.3.3.7.7.11.13.19.37.43.127.239.1933.2689.4649.10837.23311.45613.52579.

.333667.459691.909091.5274739.10838689.45121231.192143 6048294281.

.1897724226 7323558587 4485732659 126

127 3.3.18797.90679.P117

128 3.3.11.17.73.101.137.353.449.641.1409.19841.69857.976193.5882353.6187457.

.1265011073.83442 7406578561.153 4316818888 9137818369.

.515 2175252652 1326744786 9906815873 128

129 3.3.3.37.173.1527791.21 0769832431.196350 6722254397.214099201 5395526641.

.4074 2973276750 5248479163.

.1049097499 4611747848 1971728399 5603987072 3832569747 129

130 3.3.11.41.53.79.131.271.859.9091.265371653.1058313049.16 2503518711.

.5538396 9973640240 5628651064 0780600481.

.839686 2596258693 9016106022 9855716710 0076327481 130

131 3.3.80173.109517.141811693.446790173.737 0364319027.1559484553 8029429933.

.73 1772397003 1057677693.1317 5835106511 6151205213.

.1802220 6228783402 5451247081 131

132 3.3.3.7.11.11.13.23.37.67.89.101.4093.8779.9901.21649.513239.599144041.

.1052788969.1056689261.5419170769.18 3411838171.78939 0798020221.

.236100 0305507449.134462821 0313298373 132

133 3.3.239.1597.4649.202101 5460335957.111111111 1111111111.P90

134 3.3.11.493121.7986359577 8924342083.2 8213380943 1766670012 6315366099 9177245677.

.909090 9090909090 9090909090 9090909090 9090909090 9090909090 9090909091 134

xxxix Prime Factors Short 10􀀀

135 3.3.3.3.3.31.37.41.271.757.238681.333667.1577071.2906161.16357951.

.310362841.25 8360989311.44033 4654777631.418550283 0133110721.

.483418418 5972206772 3851735391 5231961831 135

136 3.3.11.73.101.103.137.4013.2071723.28559389.152533657.1491383821.

.5363222357.2 1993833369.232455 7465671829.

.655527 4617188258 3264230070 8688843668 7780323722 2654400793 136

137 3.3.2467.2535528323.10298 7975692876 2117455431.1401758 9416299060 9843314797.P74

138 3.3.3.7.11.13.37.47.139.277.2531.31051.14357 4021480139.20386 4078068831.

.54979 7184491917.111 1111111111 1111111111.246494 4534764905 9192745899.

.15953520 8632922464 4348978893 138

139 3.3.11912 4859925363.P124

140 3.3.11.29.41.71.101.239.271.281.421.3541.4649.9091.27961.123551.909091.

.3471301.4147571.13489841.121499449.6 0368344121.10259880 0232111471.

.26521279 3249617641.8 4865448387 9497562821 140

141 3.3.3.37.283.35121409.72103049 8171501831.

.316362908 7634585250 0140615403 8726382279.

.44 1506346488 3600484821 1413514191 9313523563 7149481071 6121566453 3500695867 141

142 3.3.11.290249.2415731423 9362767357 6957439049.

.4 5994811347 8868463102 2172889522 3034301839.

.31321 0694641810 6835541520 9323405389 5417069794 9315618971 6729115659 142

143 3.3.53.79.21649.513239.2823679.180523201.265371653.

.47 4286764445 9170572792 9369346443.P74 143

144 3.3.3.3.7.11.13.17.19.37.73.101.137.3169.8929.9901.52579.98641.333667.

.5882353.99990001.99 9999000001.319904 4596370769.999999 9900000001.

.11199 4624258035 6142905139 4333072012 5433979169 144

145 3.3.41.271.3191.16763.43037.62003.9605671.7 7843839397.

.1558928097 4996818911.80684370 0012696988 5399615167 0133742711.

.74490973 1145732233 9936139310 8905952897 7143716201 145

146 3.3.11.293.1 2171337159.185519384 2151350117.108266849 6453995983 7294043117.

.28 6578888976 1949979999 2259233090 8602103011.

.4920 7341634646 3269340017 3948250213 1487446637 146

147 3.3.3.37.43.239.1933.4649.63799.4715467.10838689.505885997.

.26765 2966241599.260394188 3787374089.1976 7301445981 9096356802 3014679333.

.4769337181 4649591479 9770475387 6850429427 147

148 3.3.11.101.149.3109.7253.111149.2028119.247629013.70 8840373781.

.42265 0073734453.29655734 7313446299.6 6903168666 1427842829.

.22 1239429677 0203368013.405481405 1406277475 8071840361 148

149 3.3.12517.53559 6779200919.P130

150 3.3.3.7.11.13.31.37.41.151.211.241.251.271.2161.4201.5051.9091.21401.25601.

.2906161.18 2521213001.7887 5943472201.15763 9855537391 9170916417 0940063151.

.1 0000099999 9999899998 9999900000 0000100001 150

Short 10+

Factorizations of 10n + 1, n _ 150

n Prime Factors

1 11

2 101

3 7.11.13

4 73.137

5 11.9091

6 101.9901

7 11.909091

8 17.5882353

9 7.11.13.19.52579

10 101.3541.27961

11 11.11.23.4093.8779

12 73.137.99990001

13 11.859.1058313049

14 29.101.281.121499449

15 7.11.13.211.241.2161.9091

16 353.449.641.1409.69857

17 11.103.4013.2 1993833369

18 101.9901.99 9999000001

19 11.90909090 9090909091

20 73.137.1676321.5964848081

21 7.7.11.13.127.2689.459691.909091

22 89.101.1052788969.1056689261

23 11.47.139.2531.54979 7184491917

24 17.5882353.999999 9900000001

25 11.251.5051.9091.7887 5943472201

26 101.521.19 0038197677 7332243781

27 7.11.13.19.52579.70541929.1 4175966169

28 73.137.7841.1 2752200102 0150503761

29 11.59.1540832 0493066255 7781201849

30 61.101.3541.9901.27961.4188901.39526741

31 11.9090909090 9090909090 9090909091

32 19841.976193.6187457.83442 7406578561

33 7.11.11.13.23.4093.8779.599144041.18 3411838171

34 101.28559389.1491383821.232455 7465671829

35 11.9091.909091.4147571.26521279 3249617641

36 73.137.3169.98641.99990001.319904 4596370769

37 11.7253.42265 0073734453.29655734 7313446299

38 101.72281703 6322379041.136977818 7490592461

39 7.11.13.13.157.859.6397.216451.1058313049.38 8847808493

40 17.5070721.5882353.197210 6116664671 7498359681

41 11.267050278 1396266997.34 0419382980 6058997303

42 29.101.281.9901.226549.121499449.445819222 3320340849

43 11.57009401.2182600451.73061 1655657181 7748755241

44 73.137.617.16205834 8460129675 8492708265 6402106953

xl

xli Prime Factors Short 10+

45 7.11.13.19.211.241.2161.9091.29611.52579.3762091.898 5695684401

46 101.1289.1837 1524594609.41810033 0007166986 7932658901

47 11.6299.485506 7598095567.2972627 0500913900 6771611927

48 97.353.449.641.1409.69857.206209.6 6554101249.7511 8313082913

49 11.197.909091.5076141624 3655329949 1878172639 5939035533

50 101.3541.27961.60101.7019801.1410 3673319201.168058 8011350901

51 7.11.13.103.4013.2 1993833369.29 1078844423.3 7752695530 9799110357

52 73.137.1580801.63 2527440202 1507450906 2241224544 3923049201

53 11.90 9090909090 9090909090 9090909090 9090909090 9090909091

54 101.109.9901.153469.99 9999000001.597795771 5633453386 6654838281

55 11.11.23.331.4093.5171.8779.9091.2 0163494891.3187 2784116567 4579776721

56 17.113.5882353.7376575589 6403138401.1199683 6914484637 0226083377

57 7.11.13.1458973.90909090 9090909091.7532018062 7132846254 7977919407

58 101.349.38861.618049.1181 1806375201 8364086796 3573625866 9583187541

59 11.1889.10 9080584206 8098677837.4411 9227709960 7410964453 5362851087

60 73.137.1676321.99990001.5964848081.100 0099999998 9998999900 0000010001

61 11.81131.112052 2253011683 6855321528 2578904375 7514502359 2596037161

62 101.2049349.4831 2854955451 2237305554 5883590398 2239730714 9685578249

63 7.7.11.13.19.127.2689.52579.459691.909091.5274739.

.1897724226 7323558587 4485732659 63

64 1265011073.153 4316818888 9137818369.515 2175252652 1326744786 9906815873

65 11.131.859.9091.1058313049.839686 2596258693 9016106022 9855716710 0076327481

66 89.101.9901.1052788969.1056689261.5419170769.78939 0798020221.236100 0305507449

67 11.909090 9090909090 9090909090 9090909090 9090909090 9090909090 9090909091

68 73.137.152533657.655527 4617188258 3264230070 8688843668 7780323722 2654400793

69 7.11.13.47.139.2531.31051.14357 4021480139.54979 7184491917.

.246494 4534764905 9192745899 69

70 29.101.281.421.3541.27961.3471301.13489841.121499449.6 0368344121.

.8 4865448387 9497562821 70

71 11.290249.31321 0694641810 6835541520 9323405389 5417069794 9315618971 6729115659

72 17.8929.5882353.999999 9900000001.11199 4624258035 6142905139 4333072012 5433979169

73 11.293.108266849 6453995983 7294043117.28 6578888976 1949979999 2259233090 8602103011

74 101.149.3109.111149.70 8840373781.6 6903168666 1427842829.

.405481405 1406277475 8071840361 74

75 7.11.13.211.241.251.2161.5051.9091.7887 5943472201.

.1 0000099999 9999899998 9999900000 0000100001 75

76 73.137.457.1403417.524080865 6722481737.

.29747 8330786365 6284148053 0529030248 3555043017 76

77 11.11.23.463.4093.8779.24179.590437.909091.7444361.453940262 7853030477.

.49 2463016031 5726207887 77

78 101.521.3121.9901.5339 7071018461.19 0038197677 7332243781.

.6 0605178603 1039803398 5611921721 78

79 11.1423.9615060929.

.66443 1745414905 7909799751 0158021076 9583929389 7601150694 9065646573 79

80 353.449.641.1409.69857.1634881.18453761.94 7147262401.

.349954396 0401225779 2804159621 4187605761 80

81 7.11.13.19.1459.52579.70541929.2458921051.1 4175966169.45650238 2570032651.

.6106 0038608985 8349939139 81

82 101.68389.P76

83 11.167.997.3565183.2097307081.774209824 7001476863.

.94 3176903141 3300684826 0290096029 4299878841 83

84 73.137.7841.99990001.1 1189053009.60381242 9055411913.1 2752200102 0150503761.

.1 4802942340 0750506553 84

Short 10+ Prime Factors xlii

85 11.103.4013.9091.87211.787223761.2 1993833369.

.1 6022079482 1014452066 7419183035 8091766438 6555934641 85

86 101.338669.P79

87 7.11.13.59.63 8453709757.13508 0726389891.1540832 0493066255 7781201849.

.1 2741947328 9814847176 6404179653 87

88 17.5882353.10100113.

.990 0879227786 8584242572 2365680473 0798555422 1027131082 5918482298 2673560177 88

89 11.179.1214723 7304901893.

.4180967272 6732520322 9119091718 8955510245 8741800011 6483993107 7197586653 89

90 61.101.181.3541.9901.27961.4188901.39526741.99 9999000001.

.49 9943754145 3012143121.11050 9779500299 4798105101 90

91 11.859.909091.21705503.1058313049.

.50678 3874117038 8910175912 5785290439 8943899203 8562709650 1794498837 91

92 73.137.2393.P85

93 7.11.13.373.44641.3590254957.9090909090 9090909090 9090909091.

.1838 1907262281 2446331581 9067778696 6663091011 93

94 101.45121.2144906157 5094116844 2491377407 8958939881.

.102303764 3093214557 6513331204 2298021317 2396059301 94

95 11.9091.181 2604116731.12145 0506296081.90909090 9090909091.

.499673 1930447843 6761858439 5974662149 1531100801 95

96 193.769.19841.976193.6187457.83442 7406578561.125322453 5459902849.

.5 3763491189 9672213585 7554610727 9034709697 96

97 11.1025 2736135461 3106010527.323 3384348910 3408917347 5790125293.

.2 7422699366 0546216832 9562307947 1066588881 97

98 29.101.281.121499449.P84

99 7.11.11.13.19.23.4093.8779.52579.599144041.7093127053.18 3411838171.

.1 4112252487 7886182282 2335393177 9614493830 5111168717 99

100 73.137.401.1201.1601.1676321.5964848081.

.12 9694419029 0577505513 8577118456 4274499075 7009476567 5782153729 1527196801 100

101 11.607.809.1213.1327067281.P83

102 101.409.3061.9901.5969449.28559389.134703241.1491383821.22597 4065503889.

.232455 7465671829.443980004 7900799756 9751764249 102

103 11.1237.44092859.102860539.984385009.61205 3256358933.

.1827 2511486652 1155647161.1471865 4539938553 0266088761 4137521979 103

104 17.1249.49297.300977.648961.5882353.2 4922778781 8677482257.

.3336327 6643840901 1274705987 0264076396 7004230553 6743429073 104

105 7.7.11.13.127.211.241.2161.2689.9091.459691.909091.4147571.2 9970369241.

.166137 8260814161.26521279 3249617641.182 7616884682 1336356291 105

106 101.1061.5051749.245391150 2148752495 0268580742 1982149521.

.752770 4835280872 9626679875 8529014480 3454017356 9840168229 106

107 11.1499.28463.74687.392263.795653.P82

108 73.137.3169.98641.99990001.319904 4596370769.1726 2900089915 0450017746 3302688697.

.579276943 4981542821 2368699988 1829009033 108

109 11.333878 6746233023.14060959 6838642862 6740593300 0927102019.

.193643 8332114871 9295180578 8533257418 5585898784 8620134943 109

110 89.101.661.3541.18041.27961.148721.1052788969.1056689261.1121407321.

.13959003 7091632724 5555441901.36 3805450299 5320595637 7406702261 110

111 7.11.13.223.4663.7253.42265 0073734453.29655734 7313446299.

.21 6060644986 9150524620 0058094681.48911 6891108913 0370617419 3415115219 111

112 353.449.641.673.1409.69857.4 3735845217.

.217860610 4520311215 9848927995 0204653537.

.15594 4009296214 0541006269 1600379440 7157304353 112

113 11.4973.4426889.P102

114 101.229.2281.4789.9901.304077901.5287 5286008709.72281703 6322379041.

.73965389 3349540289.136977818 7490592461.339 5073642066 1075851541 114

115 11.47.139.691.2531.9091.54979 7184491917.P86

xliii Prime Factors Short 10+

116 73.137.233.355193.2 1591416633.17468 7398484984 3803932993 5679794457.

.3203269941 6316994338 4295066992 4393166558 4097965489 0345228609 116

117 7.11.13.13.19.157.859.6397.52579.216451.461917.60034573.1058313049.

.38 8847808493.360968001 5682889556 8286578224 8182587198 1791499540 1933354161 117

118 101.430148941.P108

119 11.103.4013.909091.1868879293.2 1993833369.56 7332047267 0315859129.

.103746 6478304215 5124248643 0622636901 0022369715 4999072471 7454338463 119

120 17.5070721.5882353.1132716961.999999 9900000001.197210 6116664671 7498359681.

.2812599 8524843779 0051014401.313885064 3843375292 7908678241 120

121 11.11.11.23.4093.4357.8779.25169.1485397.1025 0298143135 9171598893.

.54 4471001372 5792963322 9165267564 6774644208 2652464055 9883408623 7345292487 121

122 101.1587221.8 1183810541.10 1444162656 0371517458 7855838589 2753596849.

.75 7433887682 6097411632 7848920184 3375280594 6178818153 9337429709 122

123 7.11.13.739.148339.16419517.267050278 1396266997.34 0419382980 6058997303.

.61051 7960355229 6927117127 4876554178 5045446837 6324892385 3725596423 123

124 73.137.1489.64 0543322297.2790 8132670449.3847 0544418223 0291105649.

.97645954 6680188464 6728718086 6355758374 2631208648 0304253688 3990817097 124

125 11.251.5051.9091.21001.162251.1 0893295001.7887 5943472201.P81

126 29.101.281.1009.9901.226549.121499449.4 3266855241.99 9999000001.

.445819222 3320340849.

.229062468 9643723122 7899575633 6201397660 4469004003 9603689929 126

127 11.3557.857772733.1094479651.1125629957.6 1689614907 3719728613.

.108 6011081377 7339731289.

.360 9953127360 3138218699 3015655675 8170515121 6702113889 127

128 257.15361.453377.P116

129 7.11.13.57009401.2182600451.73061 1655657181 7748755241.

.30 4768036847 0744910648 9460801469 5867632997.

.360 5696680890 7913827254 3216791103 8465896663 129

130 101.521.3541.27961.2311921.103149883 4064949381.1276385265 2999774041.

.19 0038197677 7332243781.121 1973050456 7977254081.

.2 7378200366 2467203108 9487008281 130

131 11.263.1397382241.30666 2501757259.5257 8637304191 4526306757.

.112 5062836800 9816875262 7601991569.

.136360808 3180796048 4111687831 9649707168 8492468691 131

132 73.137.617.2377.16369.432961.99990001.6796152793.2 4387741577.

.1 2619700217 9733470481.2838308 2652223227 9893972777.

.16205834 8460129675 8492708265 6402106953 132

133 11.909091.90909090 9090909091.2470252 3697730602 5681323889.

.6 1828645758 3221408426 6614451996 2696417487.

.7 2021403933 7461264264 9166575446 5510017877 133

134 101.269.4021.260587121.9492722820 8573594069.

.230 2527353565 3574507597 2512226288 0394277261.

.160710 3056527759 4576986582 5525217991 7706555918 8277159741 134

135 7.11.13.19.211.241.2161.6481.9091.29611.52579.3762091.70541929.

.1 4175966169.57 7603663291.898 5695684401.3102 3833790241.

.861 0583349234 3400555479 0876409101 7276717091 135

136 17.17.5882353.1 3355595217.P117

137 11.364393423.11 7651465889.44165 1480271681.67632 1006412903.

.2188012421 3685655668 0173235529.

.32445695 8063495610 1009646791 0132968264 5985939971 7968478099 137

138 101.829.1289.9901.1569889.1837 1524594609.53643053 1035337769.

.7 5710854312 9939106221.41810033 0007166986 7932658901.

.1 9108466176 7914006812 9270917199 2566565029 138

139 11.557.2503.P132

140 73.137.7841.851761.1676321.5964848081.1 2752200102 0150503761.P91

Short 10+ Prime Factors xliv

141 7.11.13.6299.344887.9127213.485506 7598095567.11 6080338393 4463712259.

.2972627 0500913900 6771611927.

.300735662 7055904894 8142559741 5127087965 9052470389 2560552659 141

142 101.569.7669.38062384 9488714809.7 7169265188 3350877868 9508504941.

.93611 3822875139 5032943162 5811490669.

.8251988265 9061966708 7624834867 1944663928 8430446081 142

143 11.11.23.859.4093.8779.51767.1058313049.2 2144088539.26 4752347289.

.1 0473010110 7272149081.P74 143

144 97.353.449.641.1409.13249.69857.206209.1067329.6 6554101249.7511 8313082913.P86

145 11.59.1451.9091.30104611.58765601.243 3146345771.1799613 2431060961.

.1540832 0493066255 7781201849.

.97862 7276654802 3124601100 8935563207 7411444912 2441851742 2691228321 145

146 101.5911541.1669 2085818029.577429 4197526381.1822027 4280260783 5615596881.P82

147 7.7.7.11.13.127.197.2689.459691.909091.

.5076141624 3655329949 1878172639 5939035533.P84 147

148 73.137.61544617.1644476 5848115921.P120

149 11.2087.96 1568303145 0065714899.

.16545960 9176797865 8661343653 2979227063 5207840943.P76 149

150 61.101.601.3541.9901.27961.60101.261301.3903901.4188901.7019801.39526741.

.16 8290119201.1410 3673319201.168058 8011350901.2507409103 8628125301.

.38654 6587957181 5645672995 8859629701 150

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