January 22, 1990 Eight "Wanted" numbers were factored on Page 59. Arjen Lenstra factored the "Most Wanted" numbers 3,241- c115 and 6,149- c108 by the Number Field Sieve algorithm. Bob Silverman factored the "More Wanted" numbers 3,236+ C92, 6,155+ C94, 11,122+ C92 and 12,121- C94 by the Quadratic Sieve algorithm and the "More Wanted" number 2,449+ C123 by the Elliptic Curve algorithm. Alford and Pomerance factored the "More Wanted" number 12,119+ c100 by the Self-Initializing Quadratic Sieve algorithm. New "Wanted" lists appear on the back of Page 59 along with the list of first four holes in each table. One this page there were several new champions for factoring Cunningham Project numbers. These are listed on the back of Page 59. Recall that a champion is one of the best TWO records in its class. Note that some new champions, such as those in # 2928 and # 2966, were not from "Wanted" numbers. We are pleased that people are trying to factor all the Cunningham numbers, not just the "Wanted" ones. The first holes done on Page 59 are listed in # 2926, 2933, 2958, 2976 and 2983. The second holes done on Page 59 are in # 2974, 2984 and 2985. The only third hole done on Page 59 is in # 2966. The fourth holes done on Page 59 are in # 2949 and 2961. The only fifth hole done on Page 59 is in # 2936. The smallest new factor reported on Page 59 has 19 digits. See # 2954. This size (19 digits) is a new high. The previous high was 18 digits for the smallest new factor on Page 55. Gary Gostin reports that he has searched up to 150000 without finding any new Mersenne primes. (I should have mentioned this when I mailed Page 58 last October. He has probably gone further by now.) I have corrected several of your addresses recently. If you move, please tell me. Keep the factors coming! Sam Wagstaff