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

Author

Zak Seidov, May 21 2005

Keywords

• nonn

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

Crossrefs

Cf. A045637.

Programs

Magma

[p: p in PrimesUpTo(25000)|  IsPrime(p+2) and IsPrime(p^2+4)]; // Vincenzo Librandi, Jan 29 2011

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]&]

PARI

a(n)=isprime(n) && isprime(n+2) && isprime(n^2+4) \\ Edward Jiang, Aug 08 2014