A248085 Initial prime of 4 primes in arithmetic progression with difference 12.

5, 7, 17, 47, 127, 227, 257, 397, 467, 607, 997, 1447, 1487, 1697, 1877, 2647, 3307, 3547, 3907, 4217, 4987, 5407, 6287, 6947, 7297, 7537, 7817, 10067, 10627, 11047, 11777, 12227, 12577, 13147, 14747, 15137, 15737, 15877, 17827, 19727, 19937, 20707, 21577, 22027, 22247, 23017, 24097, 26017

Offset: 1

Author

Zak Seidov, Oct 01 2014

Keywords

• nonn

Comments

Or, primes p such that p + 12, p + 24 and p + 36 are also primes.

Primes are not necessarily consecutive ones. A033447 is subsequence: a(92) = 111497 = A033447(1), a(144) = 258527 = A033447(2), etc.

The only case with p + 48 prime is p = 5, in all other cases p + 48 is divisible by 5.

All terms >5 are congruent to 7 (mod 10). - Zak Seidov, Jun 12 2018

Links

• Jens Kruse Andersen, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A033447.

Programs

Maple

A248085:=n->`if`(isprime(n) and isprime(n+12) and isprime(n+24) and isprime(n+36), n, NULL): seq(A248085(n), n=1..10^5); # Wesley Ivan Hurt, Oct 01 2014

Mathematica

Select[Prime[Range[1000]], PrimeQ[# + 12] && PrimeQ[# + 24] && PrimeQ[# + 36] &] (* Alonso del Arte, Oct 01 2014 *)
Select[Prime[Range[3000]],AllTrue[#+{12,24,36},PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Feb 08 2016 *)

PARI

forprime(p=5,10^5,isprime(p+12)&&isprime(p+24)&&isprime(p+36)&&print1(p","))