May 14, 1990


Two "Wanted" numbers were factored on Page 60. Arjen Lenstra factored
the "More Wanted" number 3,251- c117 by the Number Field Sieve
algorithm. With the assistance of dozens of other researchers, Arjen
Lenstra and Mark Manasse factored the "More Wanted" number 2,794L c104
by the Quadratic Sieve algorithm. We will issue new "Wanted" lists
either with Page 61 or Update # 2.4 sometime during the summer.

There was one new champion for factoring Cunningham numbers on this
page. Recall that a champion is one of the best TWO records in its
class. Arjen Lenstra and Mark Manasse and the network factored 2,484+
c111 by the Quadratic Sieve algorithm.

No first holes were done on Page 60. The second holes done on Page 60
are in # 2990 and 3003. The third holes done on Page 60 are in # 2992
and 2997. The only fourth hole done on Page 60 is in # 3045. The only
fifth hole done on Page 60 is in # 3005. On a separate sheet we list
the new champion and the first four holes in each table.

The smallest new factor reported on Page 60 has 20 digits. See # 2989,
# 3026 and # 3028. This size (20 digits) is a new high. The previous
high was 19 digits for the smallest new factor on Page 59.

Bob Silverman finished factoring the last eight 90-digit numbers from
Appendix C.  Only two c91's remain. I believe he plans to do them next.

Peter Montgomery factored 2,1192+ c357, which was the largest number in
Appendix C.

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


Keep the factors coming!


Sam Wagstaff