

A247228


Prime numbers p where 2^p1 is composite that set records for smallest prime factor of 2^p1: the smallest prime factor of 2^p1 is larger than the smallest prime factor of 2^q1 for all primes q > p.


0



11, 23, 29, 41, 59, 67, 101, 137, 149, 293, 523
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OFFSET

1,1


COMMENTS

Smallest prime factor of 2^523  1 = 160188778313202118610543685368878688932828701136501444932217468039063 (69 digits).
a(12) is probably 1237; 2^1237  1 has a 70digit prime factor and a 303digit cofactor.  Charles R Greathouse IV, Nov 27 2014


LINKS



EXAMPLE

12 is not in the sequence because 12 is not prime.
13 is not in the sequence because 2^131 is prime.
37 is not in the sequence because while the smallest prime factor of 2^291 is 233, the smallest prime factor of 2^371 is only 223.


CROSSREFS



KEYWORD

nonn,hard,more


AUTHOR



STATUS

approved



