December 11, 1987 Although Page 50 took a while to fill, it contains many beautiful factorizations. On Page 50, I wrote "A.K. Lenstra" to mean "A.K. Lenstra and M. Manasse". There was not enough room for both names. They factored four "Most Wanted" numbers, namely, 12,89+ c92, 11,97+ c97, 2,349- c93 and 10,101- c101. They also factored four "More Wanted" numbers, namely, 2,353- c101, 2,674M c87, 3,199- c86 and 12,92+ c87. Silverman factored the two "More Wanted" numbers 2,311- c87 and 10,94+ c88. Now only three numbers with base > 2 which were listed in the Cunningham-Woodall tables of 1925 remain unfactored. They are 10,97- c89, 10,109+ c93 and 11,107- c96. All three are "Wanted". You may recall that three numbers which used to be "More Wanted" were "thrown back" last summer because they are too small. As we expected, they were done quickly. Lenstra and Manasse factored 2,694M c81. Silverman factored the two c84's, 5,139- and 11,101-. The first holes which were done on Page 50 are those numbered 2377, 2382, 2395, 2396, 2397, 2398, 2406, 2413, 2414 and 2430. The second holes done on this page have numbers 2378, 2383, 2394, 2407 and 2408. Numbers 2424 and 2427 were the only third holes done. On Page 50, Silverman, Lenstra and Manasse factored the last c80's and c81's in the project. There are just two c82's left. There were new champions for both ECM and MP-QS on Page 50. Lenstra and Manasse found the 34-digit ECM champion in # 2430 and the 33-digit champion in # 2408. (They also found the 33-digit prime in # 2387 and the 32-digit primes in # 2394 and # 2398, which were champions briefly.) Silverman factored the two new MP-QS champions, the 88-digit number in # 2377 and the 87-digit number in # 2395. The former also has a new largest penultimate prime factor, one with 40 digits. The smallest new factor on Page 50 has 15 digits; see # 2379. No new factors of Fermat numbers were reported since Update 5. There was a typo in Update 5. Suyama discovered that the cofactor of F_15 was composite before Baillie did it. (See Abstr. Amer. Math. Soc. v. 5 (1984), pp. 271-272.) I have sent the complete text of the second edition to the AMS, but the printing has not yet been scheduled and I have not prepared the next update, which is Update 2.1. Please do not order the second edition until you get that update. I hope it will appear soon. Clearly, Update 2.1 will have new "Wanted" lists. You may notice that factorizations numbered 2376, 2388, 2389, 2403, 2409, 2418 and 2419 are not in the book. The higher-base tables were extended for the second edition and these numbers are from the extension. Save your copy of the first edition. It will become a rare and valuable collector's item. Keep the factors coming! Sam Wagstaff