A215642 Primes p such that there is no D such that p+D, p-D, p+2*D, p-2*D are all primes.

2, 3, 5, 7, 11, 13, 19, 23, 31, 37, 41, 43, 47, 53, 59, 61, 73, 79, 83, 103, 107, 109, 113, 127, 137, 139, 149, 151, 157, 179, 181, 199, 223, 227, 229, 239, 251, 271, 277, 281, 293, 311, 331, 349, 353, 359, 367, 379, 383, 389, 397, 401, 409, 421, 431, 439, 487, 499, 541

Offset: 1

Author

Alex Ratushnyak, Aug 18 2012

Keywords

• nonn

Comments

Conjecture: a(243)=34613 is the last term.

Examples

			17 doesn't occur in the sequence, because there is D=6: 17-12, 17-6, 17+6 and 17+12 are all primes: 5, 11, 23, 29.
		

Links

• Joerg Arndt, Table of n, a(n) for n = 1..243

Crossrefs

Cf. A078611.

Programs

Mathematica

fQ[p_] := Module[{d = 1}, While[4d < p && !(PrimeQ[p-4d] && PrimeQ[p-2d] && PrimeQ[p+2d] && PrimeQ[p+4d]), d++]; 4d > p]; Select[Prime[Range[4000]], fQ] (* T. D. Noe, Aug 20 2012 *)

PARI

N=10^9;
default(primelimit,N);
print1(2,", ");
{ forprime (p=3, N,
    D=2;  D2 = D << 1;
    t = 1;
    while ( p > D2,
        if ( isprime(p+D) & isprime(p-D) &
             isprime(p+D2) & isprime(p-D2)
        , /* then */
            t=0; break()
        );
        D += 2;  D2 += 4;
    );
    if ( t==1, print1(p,", ") );
); }
/* Joerg Arndt, Aug 20 2012 */