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devarajkandadai 2005-12-12 13:21

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

alpertron 2005-12-12 15:08

The prime factors of 1105 (the second Carmichael number) are 5, 11 and 17.

None of these prime factors are Mersenne numbers.

alpertron 2005-12-12 15:22

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.

Citrix 2005-12-12 16:04

All mersenne are base 2 prime? So all Mp are counter examples

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