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A109998 Non-Cunningham primes: primes isolated from any Cunningham chain under any iteration of 2p+-1 or (p+-1)/2. 5
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 (list; graph; refs; listen; history; text; internal format)
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
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
Sequence in context: A165285 A200321 A165981 * A328998 A031340 A172044
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

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Last modified June 13 22:21 EDT 2024. Contains 373391 sequences. (Running on oeis4.)