A236462 Primes p with prime(p) + 4 and prime(p) + 6 both prime.

19, 59, 151, 181, 211, 229, 389, 571, 877, 983, 1039, 1259, 1549, 3023, 3121, 3191, 3259, 3517, 3719, 4099, 4261, 4463, 5237, 6947, 7529, 7591, 7927, 7933, 8317, 8389, 8971, 9403, 9619, 10163, 10939, 11131, 11717, 11743, 11839, 12301

Offset: 1

Author

Zhi-Wei Sun, Jan 26 2014

Keywords

• nonn

Comments

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

See A236464 for a similar sequence.

Examples

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

Links

• Zhi-Wei Sun, Table of n, a(n) for n = 1..10000

Crossrefs

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

Programs

Mathematica

p[n_]:=p[n]=PrimeQ[Prime[n]+4]&&PrimeQ[Prime[n]+6]
n=0;Do[If[p[Prime[m]],n=n+1;Print[n," ",Prime[m]]],{m,1,10000}]
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 *)

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