A236458 Primes p with p + 2 and prime(p) + 2 both prime.

3, 5, 17, 41, 1949, 2309, 2711, 2789, 2801, 3299, 3329, 3359, 3917, 4157, 4217, 4259, 4637, 5009, 5021, 5231, 6449, 7757, 8087, 8219, 8627, 9419, 9929, 10007, 10937, 11777, 12071, 14321, 15647, 15971, 16061, 16901, 18131, 18251, 18287, 18539

Offset: 1

Author

Zhi-Wei Sun, Jan 26 2014

Keywords

• nonn

Comments

According to the conjecture in A236470, the sequence should have infinitely many terms. This is stronger than the twin prime conjecture.

See A236457 and A236467 for similar sequences.

Examples

			a(1) = 3 since 3 + 2 = 5 and prime(3) + 2 = 7 are both prime, but 2 + 2 = 4 is composite.
		

Links

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

Crossrefs

Cf. A000040, A001359, A006512, A236119, A236456, A236457, A236467, A236470.

Programs

Mathematica

p[n_]:=PrimeQ[n+2]&&PrimeQ[Prime[n]+2]
n=0;Do[If[p[Prime[m]],n=n+1;Print[n," ",Prime[m]]],{m,1,10000}]

PARI

s=[]; forprime(p=2, 20000, if(isprime(p+2) && isprime(prime(p)+2), s=concat(s, p))); s \\ Colin Barker, Jan 26 2014