December 1, 1992

Many "Wanted" numbers were factored on Page 66. From the old wanted
lists of Update 2.5, Bob Silverman factored the "Most Wanted" number
2,479- c127 by the Number Field Sieve. From the new wanted lists of
Update 2.6, Arjen Lenstra and Dan Bernstein factored the "Most Wanted"
numbers 2,488+ c145, 2,491+ c123 and 11,131- c134 and the "More Wanted"
number 2,523- c158, all by the Number Field Sieve. Bob Silverman
factored the "Most Wanted" numbers 2,481+ c122 and 2,485+ c116 by the
Number Field Sieve. A new factorer, Bruce A. Dodson, used the Elliptic
Curve Method to find factors of the "More Wanted" numbers 7,164+ c136
and 3,277+ c128. The latter left a c99 cofactor which Arjen Lenstra
finished by the Quadratic Sieve. New wanted lists are given on the
"Champions" page.

Bob Silverman factored two of the "Smaller but Needed" numbers,
12,136+ c104 and 2,802M c104. Arjen Lenstra factored 2,862L c100,
another of these numbers. A new list of "Smaller but Needed" numbers
appears on the "Champions" page.

A major factoring milestone was reached on Page 66. The last number
listed in the 1925 Cunningham-Woodall book was factored. In fact, the
last five numbers from this book were factored on Page 66. They are
2,488+, 2,479-, 2,491+, 2,481+ and 2,485+. Our next goal is to factor
all the higher base (b > 2) numbers listed in the first (1983) edition
of our book. About 40 of these numbers remain to be factored. Many of
them appear on the new wanted lists. The 10- and 12- tables from the
first edition have been finished for some time.  The first edition 11-
table was finished at # 3399 on Page 66.

There were several new champions for factoring Cunningham numbers on
this page.  Recall that a champion is one of the best two records in
its class. The new champion NFS factorization was that of 2,523- c158.
That one was also a new record penultimate factor, as were the
factorizations of 2,467- and 2,479-. A list of recent champions and the
first holes in each table is given on another sheet. We congratulate
these record holders.

The abbreviation AKL means Arjen K. Lenstra. DB is Dan Bernstein. MM is
Mark Manasse. lnfs is the Lattice Number Field Sieve. mpecm refers to
an Elliptic Curve program for the MasPar computer written by Arjen
Lenstra and Brandon Dixon.

The first holes done on Page 66 are in # 3370, 3384, 3385, 3399, 3408,
3410, 3411 and 3412. The second holes done on Page 66 are in # 3374,
3375, 3398 and 3409. The third holes done on Page 66 are in # 3361,
3368, 3397, 3402, 3413, 3416 and 3417. The fourth holes done on Page 66
are in # 3386 and 3395. The fifth holes done on Page 66 are in # 3403
and 3404.

The smallest new factor reported on Page 66 has 23 digits. See # 3358.
A 27-digit prime factor of this number was known previously.

Arjen Lenstra and I have factored the last two 100-digit numbers in
Appendix C. The last one was done on October 12, 1992. At present four
97-digit, five 98-digit and seven 99- digit numbers remain.

Harvey Dubner of Dubner Computer Systems, Inc., reports finding two new
Fermat factors. He found that 145.2 7312  + 1 divides F_7309  and that
11.2 18759  + 1 divides F_18749 .

I have corrected several of your addresses recently. If you move,
please tell me.

Keep the factors coming!


Sam Wagstaff