A counterexample-anyone-II

devarajkandadai · 2005-12-12, 13:21

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

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 2×11×61 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 2·11·61 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