OFFSET
1,1
COMMENTS
Primes p such that 2^p-1 is composite.
No proof is known that this sequence is infinite!
Assuming a conjecture of Dickson, we can prove that this sequence is infinite. See Ribenboim. - T. D. Noe, Jul 30 2012
A002515 \ {3} is a subsequence. Any proof that A002515 is infinite would imply that this sequence is infinite. - Jeppe Stig Nielsen, Aug 03 2020
REFERENCES
Paulo Ribenboim, The New Book of Prime Number Records, Springer, 1996, p. 378.
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 1..2974
Charles B. Barker, Proof that the Mersenne number M167 is composite, Bull. Amer. Math. Soc. 51 (1945), 389.
H. S. Uhler, Note on the Mersenne numbers M157 and M167, Bull. Amer. Math. Soc. 52 (1946), 178.
EXAMPLE
p=29 is included because 29 is prime, but 2^29-1 is *not* prime.
MATHEMATICA
Select[Prime[Range[70]], ! PrimeQ[2^# - 1] &] (* Harvey P. Dale, Feb 03 2011 *)
Module[{nn=15, mp}, mp=MersennePrimeExponent[Range[nn]]; Complement[ Prime[ Range[ PrimePi[Last[mp]]]], mp]] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Apr 10 2019 *)
PROG
(Magma) [p: p in PrimesUpTo(350) | not IsPrime(2^p-1)]; // Bruno Berselli, Oct 11 2012
(PARI) forprime(p=2, 1e3, if(!isprime(2^p-1), print1(p, ", "))) \\ Felix Fröhlich, Aug 10 2014
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Jeppe Stig Nielsen, Apr 20 2000
EXTENSIONS
Offset corrected by Arkadiusz Wesolowski, Jul 29 2012
STATUS
approved