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(just those submitted by Capelle)
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GIMPS has discovered a new largest known prime number: 282589933-1 (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, n-2], 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 pi(n - 2) - pi(n/2 - 1) distinct ways. Reference: An upper bound in Goldbach's problem. [Capelle]

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