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GIMPS has discovered a new largest known prime number: 2^{82589933}1 (24,862,048 digits) The prime p=197418203*2^250001 is a member of a set of three consecutive probable primes in arithmetic progression, since p6090 is probably prime, all numbers between p6090 and p are composite, all numbers between p and p+6090 are composite, and p+6090 is probably prime. As of January 2005, no larger set of three consecutive probable primes in arithmetic progression was known. A proof of the primality of p is given here. [Broadhurst]
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