July 27, 1989


Two numbers which were in the Ten "Most Wanted" list on Page lxxxvi of
the second edition were down-graded to "More Wanted" because of their
small size. These two numbers were factored on Page 57. Alford and
Pomerance factored 7,128+ c95 and Lenstra and Manasse factored 10,106+
c95.  Lenstra and Manasse also factored the "More Wanted" numbers
2,766L c104, 6,151+ c93 and 6,152+ c92 and, with the assistance of
dozens of other researchers, the "Most Wanted" number 10,122+ c103.
The latter set a new record for factoring integers by MP-QS. They also
set a new record for largest penultimate factor in factoring 2,409+
c94. The latest list of champions is given on another sheet, along with
a current list of the first four holes. (Note that these lists are
updated through part of Page 58, which appears on the same sheet.)

The first holes done on Page 57 are listed in # 2806, 2816, 2824, 2825
and 2850. The second holes done on Page 57 are in # 2812, 2841 and
2847. The third holes done on Page 57 are in # 2814, 2815, 2821, 2838
and 2854. The fourth holes done on Page 57 are in # 2852 and 2853. The
fifth holes done on Page 57 are in # 2845, 2846 and 2856.

Update 2.3 is enclosed. Note that the base 11 and base 12 tables have
been extended. Update 2.3 has new wanted lists. I neglected to update
the paragraph in Update 2.3 which tells who did which "Wanted" numbers.
I will fix it in Update 2.4.

Silverman finished the last two c87's and one c88 left in Appendix C.
There are no c89's left.  The smallest entries in Appendix C now have
90 digits.

The smallest new factor reported on Page 56 has 16 digits. See # 2809.

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


Keep the factors coming!


Sam Wagstaff