A108701 Values of n such that n^2-2 and n^2+2 are both prime.

3, 9, 15, 21, 33, 117, 237, 273, 303, 309, 387, 429, 441, 447, 513, 561, 573, 609, 807, 897, 1035, 1071, 1113, 1143, 1233, 1239, 1311, 1563, 1611, 1617, 1737, 1749, 1827, 1839, 1953, 2133, 2211, 2283, 2589, 2715, 2721, 2955, 3081, 3093, 3453, 3549, 3555, 3621, 3723, 3807

Offset

1,1

Comments

Since x^2 + 2 is divisible by 3 unless x is divisible by 3, all elements are 3 mod 6.

Intersection of A067201 and A028870. - Robert Israel, Sep 11 2014

References

David Wells, Prime Numbers, John Wiley and Sons, 2005, p. 219 (article:'Siamese primes')

Links

Nathaniel Johnston, Table of n, a(n) for n = 1..8750

Raymond A. Beauregard and E. R. Suryanarayan, Square-plus-two primes, Mathematical Gazette 85(502) 90-1.

Example

21 is on the list since 21^2 - 2 = 439 and 21^2 + 2 = 443 are primes.

Maple

select(n -> isprime(n^2-2) and isprime(n^2+2), [seq(6*i+3, i=0..1000)]); # Robert Israel, Sep 11 2014

Mathematica

Select[Range[5000], PrimeQ[#^2 - 2] && PrimeQ[#^2 + 2] &] (* Alonso del Arte, Sep 11 2014 *)

Prog

(Magma) [n: n in [3..3600 by 6] | IsPrime(n^2-2) and IsPrime(n^2+2)];  // Bruno Berselli, Apr 15 2011
(PARI) is(n)=isprime(n^2-2)&&isprime(n^2+2) \\ Charles R Greathouse IV, Jul 02 2013

Crossrefs

Subsequence of A016945.

Cf. A016945, A028870, A028873, A038599, A067201, A153974.

Sequence in context: A276967 A114271 A137164 * A064539 A029482 A174786

Adjacent sequences: A108698 A108699 A108700 * A108702 A108703 A108704

Keyword

nonn,easy

Author

John L. Drost, Jun 19 2005

Extensions

Terms corrected by Charles R Greathouse IV, Sep 11 2014

Status

approved