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A216590
Primes p with property that there exists a number d>0 such that numbers p-k*d, k=1...7, are seven primes.
1
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
1,1
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.
EXAMPLE
1669 is in the sequence because with d=210: 1459, 1249, 1039, 829, 619, 409, 199 are all primes.
PROG
(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
CROSSREFS
KEYWORD
nonn
AUTHOR
Alex Ratushnyak, Sep 09 2012
STATUS
approved