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Primes p with p + 2, prime(p) + 2, prime(prime(p)) + 2 and prime(prime(prime(p))) + 2 all prime.
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%I #11 Jan 27 2014 02:53:10

%S 41609,1119047,1928621,2348579,2371709,3406727,4098569,4204817,

%T 4438997,5561819,6161159,6293297,8236439,8736701,8890667,8951387,

%U 9231329,9390077,10492457,10619897,11255729,11514719,11769479,11920661,12316697

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

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

%H Zhi-Wei Sun, <a href="/A236482/b236482.txt">Table of n, a(n) for n = 1..100</a>

%e 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.

%t p[n_]:=p[n]=PrimeQ[n+2]&&PrimeQ[Prime[n]+2]&&PrimeQ[Prime[Prime[n]]+2]&&PrimeQ[Prime[Prime[Prime[n]]]+2]

%t n=0;Do[If[p[Prime[m]],n=n+1;Print[n," ",Prime[m]]],{m,1,10^6}]

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

%K nonn

%O 1,1

%A _Zhi-Wei Sun_, Jan 26 2014