A236484 Primes p with p + 2, prime(p) + 2, prime(prime(p)) + 2, prime(prime(prime(p))) + 2, prime(prime(prime(prime(p)))) + 2 all prime.

2371709, 3406727, 8890667, 45809639, 57219497, 58674437, 73793831, 78934589, 159935561, 207223409

Offset: 1

Author

Zhi-Wei Sun, Jan 27 2014

Keywords

• nonn

Comments

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

Examples

			a(1) =  2371709 with  2371709, 2371709 + 2 = 2371711, prime(2371709) + 2 = 38917889 + 2 = 38917891, prime(38917889) + 2 =  754394519 + 2 = 754394521, prime(754394519) + 2 = 16978533527 + 2 = 16978533529 and prime(16978533527) + 2 =  437397516929 + 2 = 437397516931 all prime.
		

Links

• Zhi-Wei Sun, Table of n, a(n) for n = 1..10

Crossrefs

Cf. A000040, A001359, A006512, A236481, A236482.

Programs

Mathematica

p[n_]:=p[n]=PrimeQ[n+2]&&PrimeQ[Prime[n]+2]&&PrimeQ[Prime[Prime[n]]+2]&&PrimeQ[Prime[Prime[Prime[n]]]+2]&&PrimeQ[Prime[Prime[Prime[Prime[n]]]]+2]
n=0;Do[If[p[Prime[m]],n=n+1;Print[n," ",Prime[m]]],{m,1,10^7}]