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%I #17 Nov 29 2014 13:36:40
%S 11,23,29,41,59,67,101,137,149,293,523
%N Prime numbers p where 2^p-1 is composite that set records for smallest prime factor of 2^p-1: the smallest prime factor of 2^p-1 is larger than the smallest prime factor of 2^q-1 for all primes q > p.
%C Smallest prime factor of 2^523 - 1 = 160188778313202118610543685368878688932828701136501444932217468039063 (69 digits).
%C a(12) is probably 1237; 2^1237 - 1 has a 70-digit prime factor and a 303-digit cofactor. - _Charles R Greathouse IV_, Nov 27 2014
%e 12 is not in the sequence because 12 is not prime.
%e 13 is not in the sequence because 2^13-1 is prime.
%e 37 is not in the sequence because while the smallest prime factor of 2^29-1 is 233, the smallest prime factor of 2^37-1 is only 223.
%Y Cf. A054723.
%K nonn,hard,more
%O 1,1
%A _J. Lowell_, Nov 27 2014