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GIMPS has discovered a new largest known prime number: 2^{82589933}1 (24,862,048 digits) The largest known Wieferich prime: 3511^{2} divides 2^{3511  1}  1. The only known Wieferich emirp. [Loungrides] The smallest emirp formed by concatenating the ordered factors of a sphenic number (i.e., 165 = 3*5*11). [Loungrides] sqrt(351115*7#) and sqrt(3511+7#) produce a pair of invertible primes, 19 and 61. [Galliani]
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