A059762 Initial primes of Cunningham chains of first type with length exactly 3. Primes in A059453 that survive as primes just two "2p+1 iterations", forming chains of exactly 3 terms.

41, 1031, 1451, 1481, 1511, 1811, 1889, 1901, 1931, 3449, 3491, 3821, 3911, 5081, 5441, 5849, 6101, 6131, 7151, 7349, 7901, 8969, 9221, 10691, 10709, 11171, 11471, 11801, 12101, 12821, 12959, 13229, 14009, 14249, 14321, 14669, 14741, 15161

Offset: 1

Author

Labos Elemer, Feb 20 2001

Keywords

• nonn

Comments

Primes p such that {(p-1)/2, p, 2p+1, 4p+3, 8p+7} = {composite, prime, prime, prime, composite}.

Examples

			41 is a term because 20 and 325 are composites, and 41, 83, and 167 are primes.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000
• Chris Caldwell's Prime Glossary, Cunningham chains.
• Warut Roonguthai, Yves Gallot's Proth.exe and Cunningham Chains.
• Eric Weisstein's World of Mathematics, Cunningham Chain.

Crossrefs

Cf. A023272, A023302, A023330, A005384, A005385, A059452, A059453, A059454, A059455, A007700.

Programs

Mathematica

ipccQ[n_]:=Module[{c=(n-1)/2},PrimeQ[NestList[2#+1&,c,4]]=={False, True, True, True, False}]; Select[Prime[Range[2000]],ipccQ] (* Harvey P. Dale, Nov 10 2014 *)

Extensions

Definition corrected by Alexandre Wajnberg, Aug 31 2005

Offset corrected by Amiram Eldar, Jul 15 2024