A062718 p and p^2 + 6 are both prime.

5, 11, 19, 31, 61, 79, 89, 109, 131, 151, 199, 269, 331, 401, 431, 569, 709, 859, 929, 941, 971, 991, 1039, 1249, 1319, 1361, 1409, 1451, 1531, 1549, 1559, 1571, 1601, 1619, 1699, 1879, 1901, 1999, 2069, 2081, 2089, 2111, 2179, 2341, 2399, 2411, 2621

Offset: 1

Author

Jason Earls, Jul 14 2001

Keywords

• nonn

Comments

The only common term with A137270 is 5. - Zak Seidov, Jun 16 2015

First cases of two, three and four consecutive primes are {2069,2081}, {3041,3049,3061} and {3403531,3403549,3403559,3403571}. - Zak Seidov, Jun 16 2015

Links

• Harry J. Smith, Table of n, a(n) for n=1..1000

Crossrefs

Cf. A137270. - Zak Seidov, Jun 16 2015

Programs

Magma

[p: p in PrimesUpTo(3000) |IsPrime(p^2+6)]; // Vincenzo Librandi, Jun 16 2015

Mathematica

Select[Prime[Range[400]], PrimeQ[#^2 + 6] &] (* Vincenzo Librandi, Jun 16 2015 *)

PARI

je=[]; for(n=1,700, if(isprime(prime(n)^2+6),je=concat(je, prime(n)))); je

PARI

{ n=0; for (m=1, 10^9, if (isprime(prime(m)^2 + 6), write("b062718.txt", n++, " ", prime(m)); if (n==1000, break)) ) } \\ Harry J. Smith, Aug 09 2009