October 5, 1989 Seven "Wanted" numbers were factored on Page 58. Lenstra and Manasse factored the "Most Wanted" numbers 2,373+ c108 and 3,239- c107 and the "More Wanted" number 7,149+ c122 by the Number Field Sieve, a new factoring algorithm. They also factored the "Most Wanted" number 11,118+ c112 by ecm and mp-qs, the "More Wanted" number 5,178+ c124 by ecm, and, with the assistance of dozens of other researchers, the "Most Wanted" number 2,361+ c103. Alford and Pomerance factored the "More Wanted" number 11,128+ c92 by the Self-Initializing Quadratic Sieve. These factorizations created several new champions for factoring Cunningham Project numbers. These are listed on the back of Page 58. Recall that a champion is one of the best TWO records in its class. The factorization of seven "Wanted" numbers creates the need for new "Wanted" lists. These appear on the back of Page 58 along with the list of first four holes in each table. The first holes done on Page 58 are listed in # 2859, 2860 and 2910. The second holes done on Page 58 are in # 2872, 2880, 2883, 2894, 2906 and 2920. The third holes done on Page 58 are in # 2863, 2881, 2882 and 2884. The fourth holes done on Page 58 are in # 2904 and 2907. The fifth holes done on Page 58 are in # 2864, 2865 and 2916. For the first time in several decades the largest known prime number is not a Mersenne prime. John Brown, Landon Curt Noll, Bodo Parady, Gene Smith, Joel Smith and Sergio Zarantonello at Amdahl discovered the prime 391581*2^216193 - 1, which is a bit larger than the largest known Mersenne prime 2^216091 - 1. They also discovered two large Sophie Germain prime pairs p and 2p + 1. Both numbers are prime when p = 53373*2^4203 - 1 and when p = 296385*2^4251 - 1. They also discovered three large twin prime pairs, the largest being p = 1706595*2^11235 - 1 and p + 2. I have been using Peter Montgomery's ecm program to find many factors during the past few years. He deserves credit for their discovery, too. The smallest new factor reported on Page 58 has 17 digits. See # 2889. I have corrected several of your addresses recently. If you move, please tell me. Keep the factors coming! Sam Wagstaff