I just found the largest known Sophie Germain prime 72021.2^23630-1. It is = 3 (mod 4), then, because of the classical result of Euler, 2p+1=72021.2^23631-1 divides the Mersenne number M(72021.2^23630-1). Happy hunting, Yves e-mail: [EMAIL PROTECTED] WWW page: http://perso.wanadoo.fr/yves.gallot
