A167119 -id:A167119 - cp's OEIS frontend

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

Klaus Brockhaus, Oct 28 2009

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

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

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.

[ 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) } } ];

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

A167135 Primes congruent to {2, 3, 5, 7, 11} mod 12.

Original entry on oeis.org

2, 3, 5, 7, 11, 17, 19, 23, 29, 31, 41, 43, 47, 53, 59, 67, 71, 79, 83, 89, 101, 103, 107, 113, 127, 131, 137, 139, 149, 151, 163, 167, 173, 179, 191, 197, 199, 211, 223, 227, 233, 239, 251, 257, 263, 269, 271, 281, 283, 293, 307, 311, 317, 331, 347, 353, 359

Offset: 1

Klaus Brockhaus, Oct 28 2009

Primes p such that p mod 12 is prime.
Primes of the form 12*n+r where n >= 0 and r is in {2, 3, 5, 7, 11}.
Except for the prime 2, these are the primes that are encountered in the set of numbers {x, f(f(x))} where x is of the form 4k+3 with k>=0, and where f(x) is the 3x+1-problem function, and f(f(x)) the second iteration value. Indeed this sequence is the set union of 2 and A002145 (4k+3 primes) and A007528 (6k+5 primes), since f(f(4k+3))=6k+5. Equivalently one does not get any prime from A068228 (the complement of the present sequence). - Michel Marcus and Bill McEachen, May 07 2016

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

Subsequences: A002145, A007528. Complement: A068228.

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.

[ p: p in PrimesUpTo(760) | p mod 12 in {2, 3, 5, 7, 11} ];

[ p: p in PrimesUpTo(760) | exists(t){ n: n in [0..p div 12] | exists(u){ r: r in {2, 3, 5,7, 11} | p eq (12*n+r) } } ];

isA167135  := n -> isprime(n) and not modp(n, 12) != 1:
select(isA167135, [$1..360]); # Peter Luschny, Mar 28 2018

Select[Prime[Range[400]],MemberQ[{2,3, 5, 7, 11},Mod[#,12]]&] (* Vincenzo Librandi, Aug 05 2012 *)
Select[Prime[Range[72]], Mod[#, 12] != 1 &] (* Peter Luschny, Mar 28 2018 *)

A215161 Primes congruent to {2, 3, 5, 7, 11} mod 17.

Original entry on oeis.org

2, 3, 5, 7, 11, 19, 37, 41, 53, 71, 73, 79, 107, 109, 113, 139, 173, 181, 211, 223, 241, 257, 277, 283, 311, 313, 317, 347, 359, 379, 419, 449, 461, 479, 487, 521, 547, 563, 617, 619, 631, 653, 683, 691, 719, 733, 751, 787, 821, 823, 827, 853, 857, 887, 929

Offset: 1

Vincenzo Librandi, Aug 05 2012

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

Cf. A000040, A167119, A167135.

[ p: p in PrimesUpTo(1000) | p mod 17 in {2, 3, 5, 7, 11} ];

Select[Prime[Range[400]],MemberQ[{2,3, 5, 7, 11},Mod[#,17]]&]

A215162 Primes congruent to {2, 3, 5, 7, 11} mod 19.

Original entry on oeis.org

2, 3, 5, 7, 11, 41, 43, 59, 79, 83, 97, 157, 163, 173, 193, 197, 211, 233, 239, 269, 271, 277, 307, 311, 347, 349, 353, 383, 401, 421, 439, 461, 463, 467, 499, 577, 613, 619, 653, 691, 727, 733, 743, 809, 839, 857, 877, 881, 919, 953, 971, 991

Offset: 1

Vincenzo Librandi, Aug 05 2012

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

Cf. A167119, A167135.

[ p: p in PrimesUpTo(1000) | p mod 19 in {2, 3, 5, 7, 11} ];

Select[Prime[Range[400]],MemberQ[{2,3, 5, 7, 11},Mod[#,19]]&]

cp's OEIS Frontend

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

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A167135 Primes congruent to {2, 3, 5, 7, 11} mod 12.

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A215161 Primes congruent to {2, 3, 5, 7, 11} mod 17.

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A215162 Primes congruent to {2, 3, 5, 7, 11} mod 19.

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