Several members of the GIMPS team responded to my request earlier this year to attempt ECM factoring of the number P773. Several thousand curves with B1=11M and B1=44M failed to find a factor. The reason for this failure can be seen in the announcement below; the earlier work gave a 50% chance of finding a 48-digit factor (had there been one) and only a very tiny chance of finding the 55-digit factor actually present. Nonetheless, the work was valuable and convinced the The Cabal that P773 was a worthy target for a record-breaking SNFS factorization. The Cabal's announcement of their success follows. Paul ---------------------------- 233-digit SNFS factorization ---------------------------- ``The Cabal'' announces the completion, on November 14, 2000, of the factorization with the Special Number Field Sieve (SNFS) of the 233-digit Cunningham number 2,773+ = 2^773 + 1 into the product of 3, 533371 and three primes of 55, 71, and 102 digits, respectively. This establishes a new record for the Special Number Field Sieve SNFS. The previous SNFS record was the 211-digit repunit number 10,211- = (10^211 - 1)/9, factored on April 8, 1999, also by the Cabal. Details are available from: ftp://ftp.cwi.nl/pub/herman/SNFSrecords/SNFS-233. _________________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.exu.ilstu.edu/mersenne/faq-mers.txt
