I think this is a size record for verifying a prime with a generic method (that doesn't use any special form information about the number). The number tested has 6959 digits (23116 bits). The test took 1.5 years. The first 25% of the elapsed time reduced the size of the number being checked by 8%. ECPP can be helped by parallelism. The most important reduction is to find D values such that P (or 4P) = X^2 + D Y^2, and then one of P+1+-2X (or +-X) can be factored as small-stuff * Q. Q is a somewhat smaller prime than P. Finding the D values can be parallelized, and factoring the P+1+xxx can also be parallelized. Rich ---------------------- From: Hans Rosenthal <hans.rosenthal@t-online.de> Subject: ECPP record: (32*10^6959-23)/99 proven prime with Primo To: NMBRTHRY@LISTSERV.NODAK.EDU I would like to inform you that I have certified the primality of (32*10^6959-23)/99, a smoothly undulating palindromic prime (SUPP) [1] having 6959 decimal digits, with the program Primo [2], Marcel Martin's implementation of the elliptic curve primality proving (ECPP) algorithm. The Primo certificate of primality is available at http://www.ellipsa.net/primo/ecpp6959.zip (4457 KB) The certification of this ordinary prime was started on 21 January 2002 with Primo 1.1.0 (tests 1 to 47) and completed on 7 July 2003 with Primo 2.0.0 (tests 48 to 953) on an AMD Athlon 1.4 GHz. There was one relevant interruption of the certification process from 29 March 2003, 6:47, until 3 April 2003, 22:45. So the total running time amounts to approximately 527 days. There is a kind of ECPP diary of the certification progress available, which was started on 9 June 2002 at 21310 (of 23116) bits (so it is not complete). This diary can be found at http://www.ellipsa.net/primo/ecpp6959_diary.txt (9 KB) I thank Marcel Martin for his help and advice, and most of all, for making the ECPP algorithm available to the world of PC users in the most comfortable form I can imagine: his marvellous Primo. Hans Rosenthal [1] http://www.worldofnumbers.com/undulat.htm# [2] http://www.ellipsa.net/primo/record.html