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GIMPS has discovered a new largest known prime number: 2^{82589933}1 (24,862,048 digits) There are only 8 positive integers n for which the number of primes < n (pi(n)) equals the number of positive integers < n relative prime to n (phi(n)). They are 2, 3, 4, 8, 10, 14, 20, and 90. [Moser] (90^{3}  1)/(90  1) is a Mersenne prime. [Goormaghtigh] The smallest number n such that it can be represented as sum of each of the terms of a set of six consecutive primes, i.e., {17, 19, 23, 29, 31, 37}, with a term of another set of six consecutive primes, {73, 71, 67, 61, 59, 53}. [Loungrides]
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