From owner-cypherpunks@toad.com Mon Sep 25 10:50:51 1995Received: from minbne.mincom.oz.au by orb.mincom.oz.au with SMTP id AA10562  (5.65c/IDA-1.4.4 for eay); Wed, 27 Sep 1995 19:41:55 +1000Received: by minbne.mincom.oz.au id AA19958  (5.65c/IDA-1.4.4 for eay@orb.mincom.oz.au); Wed, 27 Sep 1995 19:34:59 +1000Received: from relay3.UU.NET by bunyip.cc.uq.oz.au with SMTP (PP);          Wed, 27 Sep 1995 19:13:05 +1000Received: from toad.com by relay3.UU.NET with SMTP id QQzizb16156;          Wed, 27 Sep 1995 04:48:46 -0400Received: by toad.com id AA07905; Tue, 26 Sep 95 06:31:45 PDTReceived: from by toad.com id AB07851; Tue, 26 Sep 95 06:31:40 PDTReceived: from servo.qualcomm.com (servo.qualcomm.com [129.46.128.14])           by cygnus.com (8.6.12/8.6.9) with ESMTP id RAA18442           for <cypherpunks@toad.com>; Mon, 25 Sep 1995 17:52:47 -0700Received: (karn@localhost) by servo.qualcomm.com (8.6.12/QC-BSD-2.5.1)           id RAA14732; Mon, 25 Sep 1995 17:50:51 -0700Date: Mon, 25 Sep 1995 17:50:51 -0700From: Phil Karn <karn@qualcomm.com>Message-Id: <199509260050.RAA14732@servo.qualcomm.com>To: cypherpunks@toad.com, ipsec-dev@eit.comSubject: Primality verification neededSender: owner-cypherpunks@toad.comPrecedence: bulkStatus: ROX-Status: Hi. I've generated a 2047-bit "strong" prime number that I would like touse with Diffie-Hellman key exchange. I assert that not only is this number'p' prime, but so is (p-1)/2.I've used the mpz_probab_prime() function in the Gnu Math Package (GMP) version1.3.2 to test this number. This function uses the Miller-Rabin primality test.However, to increase my confidence that this number really is a strong prime,I'd like to ask others to confirm it with other tests. Here's the number in hex: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 generator, g, for this prime is 2.Thanks!Phil Karn