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GIMPS has discovered a new largest known prime number: 2^{82589933}1 (24,862,048 digits) In 1944, Linnik proved that prime(k) < k^L, where L is an absolute constant which is now called Linnik's constant. In 1957, Pan claimed L <= 10000. In 1958, he was the first to prove that L <= 5448. [Post]
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