A228857 Odd primes p > 3 for which 14*p+1 is also prime.

5, 17, 47, 53, 59, 83, 107, 113, 149, 167, 173, 239, 269, 353, 419, 443, 449, 503, 509, 563, 587, 599, 647, 659, 677, 719, 797, 827, 929, 947, 977, 983, 1097, 1103, 1109, 1187, 1193, 1223, 1229, 1259, 1289, 1367, 1409, 1427, 1433, 1439, 1493, 1523, 1667

Offset: 1

Author

Ant King, Sep 06 2013

Keywords

• nonn

Comments

In 1823, Legendre proved that the first case of Fermat’s Last Theorem is true for all exponents that are members of this sequence (see Ribenboim’s reference, p.112).

Examples

			As both 5 and 14*5 + 1 = 71 are prime, then 5 is a member of this sequence.
		

References

• Paulo Ribenboim; Fermat’s Last Theorem For Amateurs, Springer-Verlag, New York, Inc., (1999).

Crossrefs

Cf. A005384, A023212, A023228, A023237, A155943.

Programs

Magma

[p: p in PrimesInInterval(5,2000) |IsPrime(14*p+1)]; // Vincenzo Librandi, Sep 18 2016

Mathematica

Select[Prime[Range[3,1667]],PrimeQ[14#+1] &]

PARI

lista(nn) = forprime(p=5, nn, if(isprime(14*p+1), print1(p, ", "))); \\ Altug Alkan, Sep 18 2016