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GIMPS has discovered a new largest known prime number: 2^{82589933}1 (24,862,048 digits) Call this prime P. Then Q=16*P15 and R=(P1)*(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^Na) for every positive integer a. Proof: http://listserv.nodak.edu/scripts/wa.exe?A2=ind0212&L=nmbrthry&P=R2 [Broadhurst]
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