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GIMPS has discovered a new largest known prime number: 2^{82589933}1 (24,862,048 digits) The smallest prime factor of the smallest composite 2 and 3SPRP (strong probable prime). The largest member in a set of twin primes generated by the formula (N^3 + 11N) + 1, for N = 1 to 9. [Homewood] The largest 3digit prime abc with distinct digits such that a^a + b^b + c^c is prime. [Loungrides] The summatory Liouville function reaches a maximum value of 829 in the region where the PĆ³lya conjecture first fails.
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