A059761 Initial primes of Cunningham chains of first type with length exactly 2. Primes in A059453 which survive as primes only one "2p-1 iteration", forming chains of exactly 2 terms.

3, 29, 53, 113, 131, 173, 191, 233, 239, 251, 281, 293, 419, 431, 443, 491, 593, 641, 653, 659, 683, 743, 761, 809, 911, 953, 1013, 1049, 1103, 1223, 1289, 1499, 1559, 1583, 1601, 1733, 1973, 2003, 2069, 2129, 2141, 2273, 2339, 2351, 2393, 2399, 2543

Offset

1,1

Links

Harvey P. Dale, Table of n, a(n) for n = 1..1000

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

Formula

{(p-1)/2, p, 2p+1, 4p+3} = {composite, prime, prime, composite}

Example

53 is here because 26 and 215 are composites,53 and 107 are primes

Mathematica

ccftQ[p_]:=Boole[PrimeQ[{(p-1)/2, p, 2 p+1, 4 p+3}]]=={0, 1, 1, 0}; Select[ Prime[ Range[400]], ccftQ] (* Harvey P. Dale, Jun 19 2021 *)

Crossrefs

A023272, A023302, A023330, A005384, A005385, A059452-A059455, A007700.

Sequence in context: A228613 A071150 A107189 * A210360 A049437 A171409

Adjacent sequences: A059758 A059759 A059760 * A059762 A059763 A059764

Keyword

nonn

Author

Labos Elemer, Feb 20 2001

Status

approved