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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 'Firoozbakht': (Click here to show all) (8^8+88888)/8 is prime. Note that eight 8s are used. [Firoozbakht]((0)! + (1)! + ... + (k)!) is prime only for k = 1,2,..,8 (composite for k>8). [Firoozbakht] For n > 8, prime(n) > (n) + sigma(n), so 8 is the only number n such that prime(n) = (n) + sigma(n). [Firoozbakht]
(There is one curio for this number that has not yet been approved by an editor.)
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