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A216468
Primes p with property that there exists a number d>0 such that numbers p-k*d, k=1...6, are six primes.
7
907, 1307, 1439, 1459, 1669, 1879, 2089, 2141, 2351, 2713, 4139, 4759, 4969, 5179, 5417, 6047, 6101, 6353, 6779, 6793, 7919, 8369, 8663, 9049, 9349, 9491, 9533, 9623, 9769, 10099, 10691, 10883, 11083, 11213, 11369, 11399, 11621, 11789, 11887, 11923, 12097, 12119
OFFSET
1,1
COMMENTS
Conjecture: only 312722 primes are not in the sequence: 2, 3, ..., 198702899.
EXAMPLE
907 is in the sequence because with d = 150: 7, 157, 307, 457, 607, 757 are all primes.
MATHEMATICA
fQ[p_] := Module[{d = 1}, While[6*d < p && Union[PrimeQ[p - Range[6]*d]] != {True}, d++]; 6*d < p]; Select[Prime[Range[4, PrimePi[12119]]], fQ] (* T. D. Noe, Sep 07 2012 *)
PROG
(PARI) is(n)=my(t); forprime(p=2, n-20, if((n-p)%6==0 && isprime((t=(n-p)/6)+p) && isprime(2*t+p) && isprime(3*t+p) && isprime(4*t+p) && isprime(5*t+p) && isprime(n), return(1))); 0 \\ Charles R Greathouse IV, Sep 10 2014
CROSSREFS
KEYWORD
nonn
AUTHOR
Alex Ratushnyak, Sep 07 2012
STATUS
approved