A236482 Primes p with p + 2, prime(p) + 2, prime(prime(p)) + 2 and prime(prime(prime(p))) + 2 all prime.

41609, 1119047, 1928621, 2348579, 2371709, 3406727, 4098569, 4204817, 4438997, 5561819, 6161159, 6293297, 8236439, 8736701, 8890667, 8951387, 9231329, 9390077, 10492457, 10619897, 11255729, 11514719, 11769479, 11920661, 12316697

Offset: 1

Author

Zhi-Wei Sun, Jan 26 2014

Keywords

• nonn

Comments

According to the general conjecture in A236481, this sequence should have infinitely many terms.

Examples

			a(1) = 41609 with 41609, 41609 + 2 = 41611, prime(41609) + 2 = 500909 + 2 = 500911, prime(500909) + 2 = 7382957 + 2 = 7382959 and prime(7382957) + 2 = 130090109 + 2 = 130090111 all prime.
		

Links

• Zhi-Wei Sun, Table of n, a(n) for n = 1..100

Crossrefs

Cf. A000040, A001359, A006512, A236457, A236458, A236467, A236480, A236481, A236484.

Programs

Mathematica

p[n_]:=p[n]=PrimeQ[n+2]&&PrimeQ[Prime[n]+2]&&PrimeQ[Prime[Prime[n]]+2]&&PrimeQ[Prime[Prime[Prime[n]]]+2]
n=0;Do[If[p[Prime[m]],n=n+1;Print[n," ",Prime[m]]],{m,1,10^6}]