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Primes p with prime(p) + 4 and prime(p) + 6 both prime.
5

%I #11 Feb 21 2018 12:06:02

%S 19,59,151,181,211,229,389,571,877,983,1039,1259,1549,3023,3121,3191,

%T 3259,3517,3719,4099,4261,4463,5237,6947,7529,7591,7927,7933,8317,

%U 8389,8971,9403,9619,10163,10939,11131,11717,11743,11839,12301

%N Primes p with prime(p) + 4 and prime(p) + 6 both prime.

%C According to the conjecture in A236460, this sequence should have infinitely many terms.

%C See A236464 for a similar sequence.

%H Zhi-Wei Sun, <a href="/A236462/b236462.txt">Table of n, a(n) for n = 1..10000</a>

%e a(1) = 19 with 19, prime(19) + 4 = 71 and prime(19) + 6 = 73 all prime.

%t p[n_]:=p[n]=PrimeQ[Prime[n]+4]&&PrimeQ[Prime[n]+6]

%t n=0;Do[If[p[Prime[m]],n=n+1;Print[n," ",Prime[m]]],{m,1,10000}]

%t Select[Prime[Range[1500]],AllTrue[Prime[#]+{4,6},PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* _Harvey P. Dale_, Feb 21 2018 *)

%o (PARI) s=[]; forprime(p=2, 12500, if(isprime(prime(p)+4) && isprime(prime(p)+6), s=concat(s, p))); s \\ _Colin Barker_, Jan 26 2014

%Y Cf. A000040, A022005, A236456, A236457, A236458, A236460, A236464.

%K nonn

%O 1,1

%A _Zhi-Wei Sun_, Jan 26 2014