A109998 Non-Cunningham primes: primes isolated from any Cunningham chain under any iteration of 2p+-1 or (p+-1)/2.

17, 43, 67, 71, 101, 103, 109, 127, 137, 149, 151, 163, 181, 197, 223, 241, 257, 269, 283, 311, 317, 349, 353, 373, 389, 401, 409, 433, 449, 461, 463, 487, 521, 523, 557, 569, 571, 599, 617, 631, 643, 647, 677, 701, 709, 739, 751, 769, 773, 787, 797, 821

Offset

1,1

Comments

The condition that neither 2p - 1 nor 2p + 1 be prime is equivalent to ((p-1) mod 3 = 0) or ((p+1) mod 3 = 0). For example, the prime p = 2^607 - 1 is not in this sequence because p + 1 mod 3 = 2. - Washington Bomfim, Oct 30 2009

Links

Table of n, a(n) for n=1..52.

Chris Caldwell's Prime Glossary, Cunningham chains.

Douglas S. Stones, On prime chains, arXiv:0908.2166 [math.NT] [From Washington Bomfim, Oct 30 2009, edited by R. J. Mathar, Mar 01 2010]

Example

a(1) = 17 is here because 17 * 2 + 1 = 35, 17 * 2 - 1 = 33; (17+1)/2 = 9, (17-1)/2 = 8: four composite numbers.

Mathematica

nonCunninghamPrimes = {}; Do[p = Prime[n]; If[!PrimeQ[2p - 1] && !PrimeQ[2p + 1] && !PrimeQ[(p - 1)/2] && !PrimeQ[(p + 1)/2], AppendTo[nonCunninghamPrimes, p]], {n, 6!}]; nonCunninghamPrimes (* Vladimir Joseph Stephan Orlovsky, Mar 22 2009 *)

Crossrefs

Cf. A005385, A005383, A060254, A005384, A005382, A068497, A059455, A059762, A057326, A023272, A023302, A059764, A057328, A023330, A005602, A064812, A005603.

Sequence in context: A165285 A200321 A165981 * A328998 A031340 A172044

Adjacent sequences: A109995 A109996 A109997 * A109999 A110000 A110001

Keyword

easy,nonn

Author

Alexandre Wajnberg, Sep 01 2005

Extensions

Corrected and extended by Ray Chandler, Sep 02 2005

Replaced link to cached arXiv URL with link to the abstract - R. J. Mathar, Mar 01 2010

Status

approved