Object: 10^9999+33603 is prime Date: Tue, 19 Aug 2003 01:38:14 +0200 From: Jens Franke To: info (*) ellipsa (+) net Using a new parallel implementation of the Atkin-Morain elliptic curve test ECPP, we have verified the primality of 10^9999+33603, the smallest 10000-digit prime. The certificate is available by ftp: ftp://ftp.math.uni-bonn.de:pub/people/franke/p10000.cert The calculations were done using two programs, a pvm program producing the sequence of discriminants, group orders and their prime number factorization (called a downrun sequence in what follows), and the second program calculating the elliptic curves. This second step is well knwon to be massively parallel. We started to produce a downrun sequence on July 17, 2003 on 6 900MHz PIII CPUs. On July 21, the computation was moved to 12 nodes of parnass2, the LINUX cluster built at the Scientific Computing Institute in Bonn. 4 of these node had 2 800MHz CPUs, the other nodes were double PII/400MHz computers. At 8550 digits (on July 30) and 8286 digits (on July 31) we interrupted these calculations to replace the program by a faster version. On August 5, we reached 6574 digits. On August 8, we stopped the program at 3256 digits. The final calulations for the downrun sequence took about 8 hours on 8 800MHz CPUs. The CPU time spent for the actual certicicates is more difficult to estimate, since the program for this step was still under development when the calculation of the downrun sequence started, and since these calculations were done in heterogeneous environment. We estimate that it would have taken less than 140 days on a single 800MHz Athlon CPU. J. Franke T. Kleinjung T. Wirth