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A167119
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Primes congruent to 2, 3, 5, 7 or 11 (mod 13).
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5
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2, 3, 5, 7, 11, 29, 31, 37, 41, 59, 67, 83, 89, 107, 109, 137, 163, 167, 193, 197, 211, 223, 239, 241, 263, 271, 293, 317, 349, 353, 367, 379, 397, 401, 419, 421, 431, 449, 457, 479, 499, 509, 523, 557, 577, 587, 601, 613, 631, 653, 661, 683, 691, 709, 733, 739, 743, 757
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OFFSET
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1,1
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COMMENTS
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Primes which have a remainder mod 13 that is prime.
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LINKS
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EXAMPLE
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11 mod 13 = 11, 29 mod 13 = 3, 31 mod 13 = 5, hence 11, 29 and 31 are in the sequence.
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MATHEMATICA
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f[n_]:=PrimeQ[Mod[n, 13]]; lst={}; Do[p=Prime[n]; If[f[p], AppendTo[lst, p]], {n, 6, 6!}]; lst
Select[Prime[Range[4000]], MemberQ[{2, 3, 5, 7, 11}, Mod[#, 13]]&] (* Vincenzo Librandi, Aug 05 2012 *)
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PROG
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(PARI) {forprime(p=2, 740, if(isprime(p%13), print1(p, ", ")))} \\ Klaus Brockhaus, Oct 28 2009
(Magma) [ p: p in PrimesUpTo(740) | p mod 13 in {2, 3, 5, 7, 11} ]; // Klaus Brockhaus, Oct 28 2009
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CROSSREFS
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Cf. A003627, A045326, A003631, A045309, A045314, A042987, A078403, A042993, A167134, A167135: primes p such that p mod k is prime, for k = 3..12 resp.
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KEYWORD
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nonn,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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