October 2004 Torbj÷rn Alm and Jens Kruse Andersen found a prime
gap of 337446 between 7996-digit prp's (probable primes).
Sieving for small factors used the GMP (GNU Multiple Precision)
library. Prp testing of the remaining numbers was performed by
the program The gap was originally announced without primality
proofs of the gap ends p1 = 1009461925.....1170696317 and p2 =
p1 + 337446. On Alm and Andersen's suggestion they were later
kindly proved prime by Franšois Morain with his fastECPP
(elliptic curve primality proving) in March and April 2005
(announcement). Proving p1 took 75 days of cumulated CPU time on
a Xeon 2.6GHz. p2 took 65 days. The primality certificates of p1
(6.7 MB gz file) and p2 (7.0 MB) are available. At the time they
were the 9th and 10th largest ECPP proofs. It is conjectured
there are infinitely many prime gaps of all even sizes. However
it has never been proven a specific gap size exists without
finding an occurrence. 337446 became the largest specific gap
known to exist, although ther