October 1, 1990

Two "Most Wanted" numbers and five "More Wanted" were factored on Page
61.  Arjen Lenstra, Mark Manasse and a few other people factored the
most wanted number of all, 2,512+ c148, the ninth Fermat number, by the
Number Field Sieve algorithm. With the assistance of dozens of other
researchers, Arjen Lenstra and Mark Manasse factored the "Most Wanted"
number 7,146+ c111 by the Quadratic Sieve algorithm. Using the same
method, Arjen Lenstra factored the "More Wanted" numbers 2,449- c95,
7,160+ c95 and 10,134+ c98.  Bob Silverman factored the "More Wanted"
numbers 11,125+ c96 and 12,125+ c96 by the Quadratic Sieve algorithm.
We will issue new "Wanted" lists with Update # 2.4 sometime during
October. That update has been delayed because I have to rewrite some of
the programs which format it.

Now that 2,512+ c148 has been factored, all of the Ten "Most Wanted"
Factorizations listed in the Second Edition of the book have been
obtained. Only two of the "More Wanted" factorizations of the Second
Edition remain undone. They are 2,1024+ c291 and 5,256+ c134. They will
head the new Ten "Most Wanted" List in Update 2.4.

There were two new champions for factoring Cunningham numbers on this
page.  (Recall that a champion is one of the best TWO records in its
class.) These are the factorizations of 2,512+ c148 by the Number Field
Sieve and 7,146+ c111 by the Quadratic Sieve mentioned above. Both of
these champion factorizations were done by Lenstra, Manasse and some
other people. The network is presently factoring 10,142+ c116, which is
"Most Wanted" and which will be a champion for the Quadratic Sieve. We
hope to report it on Page 62.

The first holes done on Page 61 are in # 3074, 3077, 3085 and 3091. The
second holes done on Page 61 are in # 3067 and 3101. The third holes
done on Page 61 are in # 3107 and 3112. No fourth or fifth holes were
done on Page 61.

The smallest new factor reported on Page 61 has 19 digits. See # 3081
and # 3087.

Bob Silverman finished factoring the last two 91-digit numbers from
Appendix C.  Only ten c92's remain. I hope someone does them soon.

David and Gregory Chudnovsky report that the cofactor of F_18  is
composite.

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

Keep the factors coming!

Sam Wagstaff