March 1, 1984 Here is page 25 of additions to the Cunningham Table. Several of the "most wanted" factorizations have been done recently. See the other side of this sheet for the latest on the "most wanted" ones. Factors reported here were received between Nov. 3, 1983, and Mar. 1, 1984. The big news, which was reported in Time Magazine, is that the last of the original Mersenne numbers has been factored completely. Davis and Holdridge factored the C69 of 2,251-. (They did the C60 of 2,211- on page 24.) A new factoring team joins us on this page: A. O. L. Atkin and N. W. Rickert are the University of Illinois at Chicago. The "most wanted" number 11,64+ was factored twice: Atkin and Rickert did it in 47.47 minutes on an IBM 3081D using the Pollard p-1 method. Davis and Holdridge did it in 15.3 hours on a Cray-1 computer using the Kraitchik-Pomerance quadratic sieve method. These execution times do not reflect the relative speed of the two machines. The first team used a method which often fails and were lucky. The algorithm used by the second team depends much less on good fortune. Both teams found the same factors. Several months ago I sent Andrew Odlyzko all the PRP's which had not yet been proved prime. He did the primality tests for the numbers of up to about 210 digits. He sent the remaining numbers to Arjen Lenstra in Amsterdam. Arjen proved the primality of several more of them. As the result of their work, less than two dozen PRP's published in the book still have not been proved prime. They are 2,808+; 2,901+; 2,1075-; 2,844+; 2,911+; and all the ones after 2,911+. The first one has 236 digits. Both researchers used the Cohen-Lenstra version of the Adleman-Rumely-Pomerance primality test. J. W. Smith has been debugging the EPOC hardware. I have written most of the CFRAC program for it. As I have said for the past year, we hope to begin factoring numbers with it soon. It runs lots of test programs successfully. The major recent bugs have been in the communication between it and the host computer. Some of them are the fault of the host computer, which is old and in poor condition. Note to newcomers to this newsletter: I began collecting factors of the Cunningham numbers and sending them out to factorers in 1981. The factors reported on the first 22 "pages" are included in the book and the first official update to it which is in the envelope pasted in the back of your copy. The second official update will appear in the summer of 1984 and will include the factors reported in the first update. I will send it to you when it is ready. This newsletter is a preliminary notice of factorizations. I report what people tell me with very little checking. The official updates are completely checked, however. Pages 23 and 24 are enclosed. Here is a short description of the update pages: The sequence numbers in the left column count factorizations --not lines or factors -- and begin with 1 in 1981. Next comes the label and the size of the composite number which has been factored. Then comes the new factors, the discoverer(s), and the method used. "BP-rho" means the Brent-Pollard Monte Carlo method, "p-1" and "p+1" are the other Pollard methods ("p+-1" means one factor was found by each of these methods), "CFRAC" is the continued fraction method, and "QS" means quadratic sieve. Keep the factors coming! Sam Wagstaff