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 A236458 Primes p with p + 2 and prime(p) + 2 both prime. 16
 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 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified June 12 14:27 EDT 2021. Contains 344956 sequences. (Running on oeis4.)