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GIMPS has discovered a new largest known prime number: 2^{82589933}1 (24,862,048 digits) The merit of the prime gap from p to the next prime q is (qp)/log p, where log p is the typical gap by the prime number theorem. After this prime is a gap of 7868 with merit 30.04, as of 2008 the only known merit above 30 for primes above 18 digits. [Alm and Andersen]
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