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GIMPS has discovered a new largest known prime number: 2^{82589933}1 (24,862,048 digits) 807!/708!  1 is prime. [Firoozbakht] 807 is the smallest proven coefficient k such that a) k*2^n+1 & k*2^n1 are never twin primes; b) k*2^n1 & k*2^(n+1)1 are never Sophie Germain primes (personal communication from Wilfrid Keller, 20 April 2004). [Rivera]
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