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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 number of distinct representations of a number n as the sum of two primes is at most the number of primes in the interval [n/2, n2], and 210 is the largest value of n for which this upper bound is attained. In other words, 210 is the largest positive integer n that can be written as the sum of two primes in (n  2)  (n/2  1) distinct ways. Reference: An upper bound in Goldbach's problem. [Capelle]
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