

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
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OFFSET

1,1


COMMENTS

Primes p such that 2^p1 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 2^291 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^p1)]; // Bruno Berselli, Oct 11 2012
(PARI) forprime(p=2, 1e3, if(!isprime(2^p1), 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



