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A076746
List giving pairs of primes of the form 10k+3 and 10k+7.
5
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
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