December 1, 1988 On Page 53, "AKL + MM" means "A.K. Lenstra and M. Manasse". They factored the four "Most Wanted" numbers 11,107- c96, 10,109+ c93, 11,104+ c100 and 2,391- c102, and the "More Wanted" number 7,139+ c93, all by MP-QS. As you probably read in the newspaper, 11,104+ was factored by a group of about a dozen computer scientists around the world. AKL and MM wrote and distributed the program, which ran on hundreds of machines. The partial results were sent by electronic mail to DEC in Stanford where they were saved and the factorization produced. They factored 2,391- the same way, but using even more computers. The abbreviation "WRA + CP" means "'Red' Alford and Carl Pomerance". They ran MP-QS on many PC clones to factor 2,332+ c95, a "Most Wanted" number. Bob Silverman factored the "More Wanted" numbers 3,194+ c89, 11,116+ c109, 11,113- c88 and 12,104+ c89. Russell Ruby used ECM to factor the "More Wanted" number 2,368+ c93. New "Wanted" lists are enclosed. The last two numbers with base > 2 listed in the Cunningham-Woodall tables have been factored. They are 10,109+ c93 and 11,107- c96. About forty numbers with base 2 remain from the Cunningham-Woodall tables. They are the base 2 numbers with exponent < 500. Many lines of the main tables refer back to earlier lines by giving their exponents in parentheses. All but eight of the lines which are referenced this way have complete factorizations, and all of these incomplete ones are on the new "Wanted" lists. They are the base 2 numbers with exponent less than 400 (or 800 in the 2LM table). The first holes which were done on Page 53 are those numbered 2555, 2566, 2582, 2583, 2592, 2594, 2600, 2604, 2608 and 2614. The second holes which were done on Page 53 are those numbered 2562, 2568, 2572, 2574, 2589 and 2602. The only third hole factored on Page 53 was in # 2613. No fourth or fifth holes were done on this page. 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. Lenstra and Manasse and Silverman finished the last five c83's. There are nine c84's left in Appendix C. I hope they get done on Page 54. There were several new champions on Page 53. Lenstra and Manasse set new records for MP-QS and Silverman set new records for p-1/FFT. These three people and Alford and Pomerance found new largest penultimate prime factors. The list of recent champions is enclosed. We welcome the new factorers on Page 53 and wish them much success. The smallest new factor on Page 53 has 17 digits. See # 2552. The factorization of 2,2366L in # 2553 completes the factorization of the 713-digit number 2^2366 + 1, which is now the largest fully factored number in the main tables. Walter N. Colquitt reports that he and Luther Welsh, Jr. have searched all the way up to exponent 132049 without finding any more Mersenne primes. Thus, M_110503 and M_132049 are the 29th and 30th Mersenne primes in order of size. The second edition appeared in August. I have corrected several of your addresses recently. If you move, please tell me. Keep the factors coming! Sam Wagstaff