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

1,1

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.

Links

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

Example

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

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}]

Prog

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

Crossrefs

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

Sequence in context: A113275 A280080 A001572 * A131342 A005142 A165452

Adjacent sequences: A236455 A236456 A236457 * A236459 A236460 A236461

Keyword

nonn

Author

Zhi-Wei Sun, Jan 26 2014

Status

approved