A072936 Primes p that do not divide 2^x+1 for any x>=1.

2, 7, 23, 31, 47, 71, 73, 79, 89, 103, 127, 151, 167, 191, 199, 223, 233, 239, 263, 271, 311, 337, 359, 367, 383, 431, 439, 463, 479, 487, 503, 599, 601, 607, 631, 647, 719, 727, 743, 751, 823, 839, 863, 881, 887, 911, 919, 937, 967, 983, 991, 1031, 1039, 1063

Offset: 1

Author

Benoit Cloitre, Aug 20 2002

Keywords

• nonn

Comments

Also, primes p such that p^2 does not divide 2^x+1 for any x>=1.

A prime p cannot divide 2^x+1 if the multiplicative order of 2 (mod p) is odd. - T. D. Noe, Aug 22 2004

Differs from A049564 first at p=6529, which is the 250th entry in A049564 related to 279^32 =2 mod 6529, but absent here because 6529 divides 2^51+1. [From R. J. Mathar, Sep 25 2008]

References

• A. K. Devaraj, "Euler's Generalization of Fermat's Theorem-A Further Generalization", in ISSN #1550-3747, Proceedings of Hawaii Intl Conference on Statistics, Mathematics & Related Fields, 2004.

Links

• T. D. Noe, Table of n, a(n) for n=1..1000

Crossrefs

Cf. A040098, A049096, A014664 (multiplicative order of 2 mod n-th prime).

Extensions

Edited by T. D. Noe, Aug 22 2004