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

1,1

Comments

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

See A236464 for a similar sequence.

Links

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

Example

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

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 *)

Prog

(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

Crossrefs

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

Sequence in context: A139920 A182475 A142190 * A139981 A235705 A171247

Adjacent sequences: A236459 A236460 A236461 * A236463 A236464 A236465

Keyword

nonn

Author

Zhi-Wei Sun, Jan 26 2014

Status

approved