login
A059764
Initial (unsafe) primes of Cunningham chains of first type with length exactly 5. Primes in A059453 that survive as primes just four "2p+1 iterations", forming chains of exactly 5 terms.
13
2, 53639, 53849, 61409, 66749, 143609, 167729, 186149, 206369, 268049, 296099, 340919, 422069, 446609, 539009, 594449, 607319, 658349, 671249, 725009, 775949, 812849, 819509, 926669, 1008209, 1092089, 1132949, 1271849
OFFSET
1,1
COMMENTS
Primes p such that {(p-1)/2, p, 2p+1, 4p+3, 8p+7, 16p+15, 32p+31} = {nonprime, prime, prime, prime, prime, prime, composite}.
LINKS
Chris Caldwell's Prime Glossary, Cunningham chains.
EXAMPLE
2 is here because (2-1)/2 = 1/2 and 32*2+31 = 95 are not primes, while 2, 5, 11, 23, and 47 give a first-kind Cunningham chain of 5 primes which cannot be continued.
53639 is here because through <2p+1>, 53639 -> 107279 -> 214559 -> 429119 -> 858239 and the chain ends here (with this operator).
MATHEMATICA
l5Q[n_]:=Module[{a=PrimeQ[(n-1)/2], b=PrimeQ[ NestList[2#+1&, n, 5]]}, Join[{a}, b]=={False, True, True, True, True, True, False}]; Select[Range[ 1300000], l5Q] (* Harvey P. Dale, Oct 14 2012 *)
KEYWORD
nonn
AUTHOR
Labos Elemer, Feb 20 2001
EXTENSIONS
Definition corrected by Alexandre Wajnberg, Aug 31 2005
Entry revised by N. J. A. Sloane, Apr 01 2006
STATUS
approved