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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) The only prime member of a RuthAaron pair. [Caldwell]The sum of the reciprocals of the primes is infinite, but the sum of the reciprocals of the known primes is less than 5 and will always be so! [Caldwell] Every positive integer can be written as x^{2}+2y^{2}+7z^{2}+11w^{2}, except for 5. [Halmos1938] [Caldwell]
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