VIII. Introduction to the Appendices.

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Certain information relating to the entries in the main tables has been collected

in these appendices to make the main tables less cluttered.

Appendix A. This appendix contains the actual decimal digits of some prime

factors shown in abbreviated form in the main tables. Generally, these are those

primes with more than 25 decimal digits, but some as short as 21 digits are abbreviated.

Their listing here greatly shortens the main tables, where only a short

label references the actual factor. Each entry of this appendix gives the number of

decimal digits, the label, and the decimal digits of the factor, separated into groups

of ten. The numbers here and in Appendix C are listed by increasing number of

digits.

Appendix A of the _rst and second editions showed the digits of all primes

referenced by a short label in the main tables. We have greatly abbreviated this

appendix in the third edition, giving only the Mersenne primes, the divisors of

b2n +1, the factors of 10n _ 1, and the primes needed for the Short tables because

this saves much space, few readers require the actual digits of these primes, many

programs (such as Maple and Mathematica) for computing these large numbers are

readily available, and we give the full Appendix A at the web site

http://www.cerias.purdue.edu/homes/ssw/cun/index.html.

Appendix B. The information in this appendix is listed in three columns: the

length of the prime, its label, and a summary of the primality proof. The notation

used in the third column is explained in III B 3(c). All of the prime proofs were

done anew for the third edition, resulting in many proof simpli_cations. Most

proofs were done by SSW, but a few come from others such as Hugh Williams,

Richard Brent and Hiromi Suyama (their names appear in the proofs they supplied).

Fran_cois Morain gave ECPP (see IV A 3(b)) proofs of primality of the ones which

could not be done easily with the methods of III B 3(a). We are grateful to these

people for their permission to include these results in our appendix. Two asterisks

denote exponentiation in a few proof summaries. The su_x \t" on a label indicates

that the prime appears in full in the main tables and not in Appendix A.

The power of modern factoring algorithms allows one to factor p _ 1 very

quickly for p < 1060 and thus give a proof \PPL," \CMB" or \BLS7" with ease.

Therefore, we have omitted the proofs of primality of primes smaller than 60 digits.

This decision also saves space. The full Appendix B and counts of the primes of

each length in the tables and in the full Appendix A are given at the web site

mentioned above.

Appendix C. The entries in this appendix are the composite cofactors with no

more than 142 digits for the incomplete factorizations in the main tables. Those

with more than 142 digits can easily be produced by a program like Maple or

Mathematica that can handle large numbers. The full Appendix C is available

at the web site mentioned above. Each line in this appendix gives the number of

decimal digits, the label and the digits of the cofactor itself. It will be noted that

the numbers in this appendix have more than 129 digits. We are con_dent that

these numbers will be factored in the near future.

165

40 digits

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