February 2, 1989


On Page 54, "AKL + MM" means "A.K. Lenstra and M. Manasse". They
factored the three "Most Wanted" numbers 10,143- c106, 10,133+ c109
and 3,229+ c104. I found a small factor of the "More Wanted" number
2,383+ c115 and they finished it. All of these factors were found by
ECM except for the part of 10,133+ reported in # 2623. That c82 was
done by MP-QS.

Since only four "Wanted" numbers were factored since the previous
wanted lists appeared, no new "Wanted" lists are enclosed. Note,
however, that the following numbers are the first holes in their
tables: 2,445- c103, 2,404+ c121, 3,236+ c92, 7,163- c125,
10,151- c139 and 11,131- c134. Some of them will appear on the
next "Wanted" lists, which will be issued either with Page 55 or with
Update 2.3.

The first holes which were done on Page 54 are those numbered 2621 and
2624. The second holes which were done on Page 54 are those numbered
2617, 2625, 2637 and 2638. The third holes which were done on Page 54
are those numbered 2619, 2622, and 2623. The only fourth hole done on
Page 54 was in # 2642. The fifth holes which were done on Page 54 are
those numbered 2626 and 2631. A list of the current first four holes is
enclosed. On this list, the fifth hole is shown if it is "Wanted" or if
I expect it to move into the fourth position soon.

The Cunningham authors use the term "tiny" to mean an important
unfactored number which is too small to be "Wanted". We are happy when
someone factors one of these unglamorous numbers.  We are grateful to
Bob Silverman for factoring the "tinies" numbered 2617, 2625, 2637,
2638 and 2642. At present, the only outstanding tiny is 7,259L c87,
which is the last unfactored higher-base (b > 2) Aurifueillian from the
first edition.

The factorizations of 10,143- and 10,145- complete the 10- table of
the first edition. It is the first table from the first edition to
have all of its entries completely factored. The 11- table is likely
to be next to be finished, as only one entry (11,131-) remains from
the first edition. In fact, only one additional entry (11,145-)
remains undone in the second edition. This shortage of composites
prompts us to extend the base 11 tables. The extension follows the
table of first four holes on another page. I am factoring 11,153+ c86
now.

Silverman finished the last nine c84's. There are five c85's left in
Appendix C. I hope they get done on Page 55.

There were no new champions on Page 54. However, since I omitted Alford
and Pomerance from the list of champions issued with Page 53, I enclose
the corrected list of MP-QS champions.  Another error in the previous
mailing was that "AKL + MM + al" should have been listed as the
factorer for 11,107- and 10,109+ in # 2582 and # 2589, since they
had assistance from others in these factorizations.

The smallest new factor on Page 54 has 16 digits. See # 2644 and # 2659.

The factorization of 2,2274M in # 2678 completes the factorization of
the 685-digit number 2 2274  + 1.

The c329 reported in # 2669 is the largest number from the Cunningham
Project to be factored since # 2428, that is, for more than a year.

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


Keep the factors coming!


Sam Wagstaff