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GIMPS has discovered a new largest known prime number: 282589933-1 (24,862,048 digits)

+ Call this prime P. Then Q=16*P-15 and R=(P-1)*(16*P+1)/9266506659322630097+1 are also primes. As of September 2003, N=P*Q*R was the largest known Carmichael number with precisely 3 prime factors. In other words, N divides (a^N-a) for every positive integer a. Proof: [Broadhurst]

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