A216590 Primes p with property that there exists a number d>0 such that numbers p-k*d, k=1...7, are seven primes.

1669, 1879, 2089, 2351, 4969, 5179, 6047, 10883, 11923, 12097, 12143, 12329, 12539, 12763, 13049, 13183, 15413, 15923, 16187, 16547, 16741, 17189, 17581, 18481, 19993, 20201, 21433, 21727, 22303, 22483, 23021, 23053, 23831, 24023, 24749, 25579, 25633, 26111, 26561

Offset: 1

Author

Alex Ratushnyak, Sep 09 2012

Keywords

• nonn

Comments

Conjecture: only 5254157 primes are not in the sequence: 2, 3, ..., 5082095279.

Conjecture: for any k>0 there exists p0 such that for any prime p>p0 there exists a k-term arithmetic progression of primes with p at the end.

Examples

			1669 is in the sequence because with d=210: 1459, 1249, 1039, 829, 619, 409, 199 are all primes.
		

Crossrefs

Cf. A216495, A094383, A216497, A216498, A216468.

Programs

PARI

is(n)=my(t); forprime(p=2,n-26,if((n-p)%7==0 && isprime((t=(n-p)/7)+p) && isprime(2*t+p) && isprime(3*t+p) && isprime(4*t+p) && isprime(5*t+p) && isprime(6*t+p) && isprime(n), return(1))); 0 \\ Charles R Greathouse IV, Sep 10 2014