A167134 Primes congruent to {2, 3, 5, 7} mod 11.

2, 3, 5, 7, 13, 29, 47, 71, 73, 79, 101, 113, 137, 139, 157, 167, 179, 181, 211, 223, 227, 233, 269, 271, 277, 293, 311, 313, 337, 359, 379, 401, 409, 421, 431, 443, 467, 487, 491, 509, 541, 557, 563, 577, 599, 601, 607, 619, 641, 643, 673, 709, 733, 739, 751

Offset: 1

Author

Klaus Brockhaus, Oct 28 2009

Keywords

• nonn
• easy

Comments

Primes p such that p mod 11 is prime.

Primes of the form 11*n+r where n >= 0 and r is in {2, 3, 5, 7}.

2 and primes congruent to {3, 5, 7, 13} mod 22. - Chai Wah Wu, Apr 29 2025

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A003627, A045326, A003631, A045309, A045314, A042987, A078403, A042993, A167134, A167135, A167119: primes p such that p mod k is prime, for k = 3..13 resp.

Programs

Magma

[ p: p in PrimesUpTo(760) | p mod 11 in {2, 3, 5, 7} ];
[ p: p in PrimesUpTo(760) | exists(t){ n: n in [0..p div 11] | exists(u){ r: r in {2, 3, 5,7} | p eq (11*n+r) } } ];

Mathematica

Select[Prime[Range[600]],MemberQ[{2, 3, 5, 7},Mod[#,11]]&] (* Vincenzo Librandi, Aug 05 2012 *)