A076746 List giving pairs of primes of the form 10k+3 and 10k+7.

3, 7, 13, 17, 43, 47, 103, 107, 163, 167, 193, 197, 223, 227, 313, 317, 463, 467, 613, 617, 643, 647, 673, 677, 823, 827, 853, 857, 883, 887, 1093, 1097, 1213, 1217, 1303, 1307, 1423, 1427, 1483, 1487, 1663, 1667, 1693, 1697, 1783, 1787, 1873, 1877, 1993

Offset

1,1

Comments

Except for 3 and 7, all pairs are 30k+13 and 30k+17.

Is this sequence infinite?

Links

Roger L. Bagula, May 04 2008, Table of n, a(n) for n = 1..142

Example

43 and 47 are in the sequence because both are prime; 73 and 77 aren't because not both are primes.

Mathematica

a[0] = 3; a[n_] := a[n] = a[n - 1] + 10; Flatten[Table[If[PrimeQ[a[n]] && PrimeQ[a[n] + 4], {a[n], a[n] + 4}, {}], {n, 0, 1000}]] (* Roger L. Bagula, May 04 2008 *)
Flatten[Select[Table[10n+{3, 7}, {n, 0, 200}], And@@PrimeQ[#]&]] (* Harvey P. Dale, Dec 31 2013 *)

Prog

(PARI) forstep(x=3, 2000, 10, if(isprime(x) && isprime(x+4), print1(x, ", ", x+4, ", ")))
(Magma) &cat[[10*k+3, 10*k+7]: k in [0..250]| IsPrime(10*k+3) and IsPrime(10*k+7)]; // Vincenzo Librandi, Jun 17 2016

Crossrefs

Cf. A001097.

Cf. A132243, A132242, A076746.

Sequence in context: A045423 A214782 A032437 * A243706 A214696 A291661

Adjacent sequences: A076743 A076744 A076745 * A076747 A076748 A076749

Keyword

nonn

Author

Cino Hilliard, Nov 11 2002

Extensions

Edited by Don Reble, Jun 07 2003

More terms from Roger L. Bagula, May 04 2008

Status

approved