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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: http://listserv.nodak.edu/scripts/wa.exe?A2=ind0212&L=nmbrthry&P=R2 [Broadhurst]

 

  Submitted: 2003-09-27 05:28:28;   Last Modified: 2008-01-30 11:28:00.



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