A107312 Primes p such that p + 2 and p^2 + 2^2 are primes.

3, 5, 17, 137, 347, 827, 2087, 2687, 3557, 3917, 4517, 4967, 5477, 5657, 5867, 6827, 7457, 7547, 7877, 8087, 8537, 8597, 10037, 10427, 10937, 12107, 12377, 13397, 13877, 16067, 17837, 17987, 19427, 19697, 20507, 20717, 20807, 22367, 22637

Offset

1,1

Comments

Primes are lesser twins. Except a(1) and a(2), all a(n) == 7(mod 10).

Links

Edward Jiang, Table of n, a(n) for n = 1..1000

Maple

select(p -> isprime(p) and isprime(p+2) and isprime(p^2+4), [seq(2*i+1, i=1..10000)]); # Robert Israel, Aug 11 2014

Mathematica

Select[Prime[Range[3000]], PrimeQ[ #+2]&&PrimeQ[ #^2+4]&]

Prog

(Magma) [p: p in PrimesUpTo(25000)|  IsPrime(p+2) and IsPrime(p^2+4)] // Vincenzo Librandi, Jan 29 2011
(PARI) a(n)=isprime(n) && isprime(n+2) && isprime(n^2+4) \\ Edward Jiang, Aug O8 2014

Crossrefs

Cf. A045637.

Sequence in context: A288376 A096178 A348430 * A083213 A171271 A056826

Adjacent sequences: A107309 A107310 A107311 * A107313 A107314 A107315

Keyword

nonn

Author

Zak Seidov, May 21 2005

Status

approved