A216497 Primes p with property that there exists a number d>0 such that numbers p-k*d, k=1...4, are four primes.

29, 53, 127, 131, 157, 173, 197, 227, 251, 257, 271, 283, 293, 311, 353, 373, 389, 397, 421, 443, 449, 463, 479, 509, 521, 587, 607, 613, 617, 661, 673, 677, 691, 719, 757, 761, 811, 821, 823, 839, 853, 859, 863, 881, 887, 907, 911, 941, 953, 967, 983, 997, 1013

Offset: 1

Author

Alex Ratushnyak, Sep 08 2012

Keywords

• nonn

Comments

Conjecture: only 653 primes are not in the sequence: 2, 3, ..., 100291.

Examples

			29 is in the sequence because with d=6: 23, 17, 11, 5 are all primes.
		

Crossrefs

Cf. A216495, A094383, A216498, A216468.

Programs

Mathematica

prms = 4; fQ[p_] := Module[{d = 1}, While[prms*d < p && Union[PrimeQ[p - Range[prms]*d]] != {True}, d++]; prms*d < p]; Select[Prime[Range[2, PrimePi[1013]]], fQ] (* T. D. Noe, Sep 08 2012 *)

PARI

is(n)=my(t); forprime(p=2,n-12,if((n-p)%4==0 && isprime((t=(n-p)/4)+p) && isprime(2*t+p) && isprime(3*t+p) && isprime(n), return(1))); 0 \\ Charles R Greathouse IV, Sep 10 2014