September 19, 1986


Two "Most Wanted" and four "More Wanted" numbers from the lists in
Update # 4 were split on Page 46. Silverman factored 10,97+ c96 and
3,178+ c84. The latter was a new champion for mp-qs, the only new
champion on Page 46. He also factored the "More Wanted" numbers 3,256+
c111, 7,116+ c82 and 11,109- c113. Montgomery found a factor of 11,101-
c105. Its c84 cofactor remains "More Wanted".

The factorizations numbered 2121, 2122, 2131, 2135, 2137, 2142 and 2157
were of first holes in their tables. The factorizations numbered 2117,
2125, 2143, 2146, 2147 and 2174 were of second holes in their tables.
All these holes and a couple of third holes were filled by Silverman
and Montgomery.

Silverman finished the c71's on Page 46. Now the smallest entry in
Appendix C has 72 digits.

Silverman and Montgomery finished the last Aurifeuillians in the book
for bases 10, 11 and 12.  The last Aurifeuillians for bases 3 and 6
were finished on Pages 40 and 44, respectively. Now, unfactored
Aurifeuillians in the book remain only for bases 5 (one), 7 (three) and
2 (many).

Arjen Lenstra has proved the primality of the first three of the 36
PRP's remaining in Update # 4. They are 2,809+ p213, 2,1594L p213 and
2,1546M p220. Now 2,1958M prp222 is the smallest PRP remaining in
Appendix A which has not yet been proved prime.

New factors are arriving more slowly now. I do not expect Page 47 to
appear for several months. If you want it to appear sooner, then send
me some new factors.


Keep the factors coming!


Sam Wagstaff