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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 'Caldwell': (Click here to show all) Proving the Riemann Hypothesis is equivalent to showingfloor(H(n)+e^{H(n))*log(H(n)}) > σ(n),where H(n) = 1 + 1/2 + 1/3 + ... + 1/n, and σ(n) is the sum of the divisors of n. For example, when n = 17, the two sides differ by 23. [Caldwell]
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