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 A054723 Prime exponents of composite Mersenne numbers. 39
 11, 23, 29, 37, 41, 43, 47, 53, 59, 67, 71, 73, 79, 83, 97, 101, 103, 109, 113, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293, 307, 311, 313, 317, 331 (list; graph; refs; listen; history; text; internal format)
 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 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 *) 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 FrÃ¶hlich, Aug 10 2014 CROSSREFS Complement of A000043 inside A000040. Cf. A016027. Sequence in context: A138537 A271983 A136000 * A109981 A091367 A088136 Adjacent sequences:  A054720 A054721 A054722 * A054724 A054725 A054726 KEYWORD easy,nonn AUTHOR Jeppe Stig Nielsen, Apr 20 2000 EXTENSIONS Offset corrected by Arkadiusz Wesolowski, Jul 29 2012 STATUS approved

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Last modified January 19 18:27 EST 2019. Contains 319309 sequences. (Running on oeis4.)