A236457 Primes p with q = p + 2 and prime(q) + 2 both prime.

3, 5, 11, 41, 107, 311, 461, 599, 641, 1277, 1619, 1997, 2309, 2381, 2789, 3671, 4787, 5099, 6659, 6701, 6827, 7457, 7487, 8219, 8537, 8597, 9929, 10709, 11117, 12071, 12107, 12251, 13709, 17747, 18047, 18251, 18521, 22091, 22637, 23027

Offset: 1

Author

Zhi-Wei Sun, Jan 26 2014

Keywords

• nonn

Comments

According to the conjecture in A236456, this sequence should have infinitely many terms.

See A236458 for a similar sequence.

Examples

			a(1) = 3 since 3 + 2 = 5 and prime(5) + 2 = 13 are both prime, but 2 + 2 = 4 is not.
		

Links

• Zhi-Wei Sun, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000040, A001359, A006512, A236119, A236456, A236458.

Programs

Mathematica

p[n_]:=PrimeQ[n+2]&&PrimeQ[Prime[n+2]+2]
In[2]:= n=0;Do[If[p[Prime[m]],n=n+1;Print[n," ",Prime[m]]],{m,1,10000}]
Select[Prime[Range[2600]],AllTrue[{#+2,Prime[#+2]+2},PrimeQ]&] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Jun 21 2021 *)

PARI

s=[]; forprime(p=2, 24000, q=p+2; if(isprime(q) && isprime(prime(q)+2), s=concat(s, p))); s \\ Colin Barker, Jan 26 2014