mersenneforum.org A counterexample-anyone-II
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 2005-12-12, 13:21 #1 devarajkandadai     May 2004 22×79 Posts A counterexample-anyone-II I have a hunch that the factors of a Carmichael Number cannot all be Mersenne.Counterexamples are welcome. A.K. Devaraj
 2005-12-12, 15:08 #2 alpertron     Aug 2002 Buenos Aires, Argentina 32·149 Posts The prime factors of 1105 (the second Carmichael number) are 5, 11 and 17. None of these prime factors are Mersenne numbers. Last fiddled with by alpertron on 2005-12-12 at 15:10 Reason: Fix typo
 2005-12-12, 15:22 #3 alpertron     Aug 2002 Buenos Aires, Argentina 32×149 Posts If you want that all prime factors of the Carmichael number have to be Mersenne numbers, it cannot be of the known form (6k+1)(12k+1)(18k+1), where each factor is prime. But most Carmichael numbers do not have this form.
 2005-12-12, 16:04 #4 Citrix     Jun 2003 1,579 Posts All mersenne are base 2 prime? So all Mp are counter examples