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GIMPS has discovered a new largest known prime number: 2^{82589933}1 (24,862,048 digits) Chinese mathematicians (circa 500 B.C.) erroneously believed that 2(2^(n1)1) is not divisible by n if n is not prime. This was disproved by Sarrus in 1819 with n = 341, i.e., the smallest pseudoprime to base two. The smallest member of the series n(n + 1 )  1 which, if composite, is not the product of two smaller primes in the series of the form 10k  1 or 10k + 1. [McNamara]
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