V. Update to the Introduction for the Third Edition.

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The tables of the second edition contained all factors known to the authors on

June 22, 1987. Since then more than two thousand new factorizations have been

discovered. Appendix C lists the smallest composite cofactors in the tables. In the

_rst edition this appendix contained numbers with 51 to 64 digits. In the second

edition it contained numbers with 80 to 100 digits. It now contains numbers with

130 to 142 digits. The lists of \wanted" factorizations in the _rst edition had 25

numbers with 52 to 71 digits. These have all been factored. The lists of \wanted"

factorizations in the second edition had 32 numbers with 86 to 291 digits. These

have all been factored. Other \wanted" lists have since been issued and many of

their entries have been factored. The current \wanted" lists (see B below) now

contain numbers with 141 to 212 digits. All of the numbers considered in the 1925

Cunningham-Woodall book [11] have been completely factored!

The smallest probable prime (PRP) in Appendix A of the second edition had

222 digits. Prime proofs have now been completed for all prime numbers in that

appendix, as well as for primes found since 1988. In this edition we have updated

the tables and appendices to September 18, 2001, and reviewed the developments

in technology, factorization and primality testing which have produced the recent

advances. We also include a few references to recent related work which may interest

the reader.

We extended the tables with base b > 2 in the second edition, and we have

lengthened them again in the third edition. We have attempted to factor the new

numbers added to these tables using about the same e_ort that was applied to

numbers in the second edition.

The format of the tables and appendices has been changed a little in this

edition. In the _rst and second editions, all penultimate prime factors _t on a

single line, which allowed us to break lines only at multiplication dots. Because we

can now factor much larger numbers than before, some penultimate prime factors

have more than 75 digits and are given on two lines with a continuation slash (n)

at the end of the _rst line. For example, in the 2􀀀 Table one _nds the entry

571 5711:27409:69693366045316671685098712301007940958018325270028n

49548226132675916172927:P 91

The prime factor 6969 : : : 00284954 : : :2927 was too long to _t on one line and had

to be broken.

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