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GIMPS has discovered a new largest known prime number: 2^{82589933}1 (24,862,048 digits) Paul Erdős conjectured that this is the largest number n such that the positive values of n  2^{k} are all prime. 105/pi^{4} = (1 + 1/2^{4})(1 + 1/3^{4})(1 + 1/5^{4})(1 + 1/7^{4})(1 + 1/11^{4}) .... [Ramanujan] The first product of 3 distinct odd primes p. Note that p +/ 2 are primes. [Gallardo] 105 is the first degree for which the cyclotomic polynom factor are not all 1, 0 or 1. [Cristian] The largest natural number n for which all odd numbers k relatively prime to n, with 1 < k < n, are primes. It is also the largest for which 2np is prime for each prime p in [n, 2n2]. [Capelle]
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