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GIMPS has discovered a new largest known prime number: 2^{82589933}1 (24,862,048 digits) Just showing those entries submitted by 'Capelle': (Click here to show all) The smallest odd prime number that cannot be expressed as the sum of a power of two and a prime (so it is also the smallest prime that becomes composite upon changing any one of the bits in its binary expansion). [Capelle]M(127) = M(M(7)) = M(M(M(3))) = M(M(M(M(2)))). Note that M(2), M(3), M(7) and M(127) are all Mersenne primes. [Capelle] The largest known prime p such that p^{2} mod q is odd, where q is the previous prime. [Capelle] The largest known prime number that cannot be written as a sum of cubes greater than one. It's the only such prime written with two cubes concatenated. [Capelle]
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