A080841 - OEIS

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A080841

Number of pairs (p,q) of (not necessarily consecutive) primes with q-p = 6 and q < 10^n.

0, 15, 74, 411, 2447, 16386, 117207, 879908, 6849047, 54818296, 448725003, 3741217498

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OFFSET

1,2

COMMENTS

Note that one has to be careful to distinguish between pairs of consecutive primes (p,q) with q-p = 6 (A031924), and pairs of primes (p,q) with q-p = 6 (A023201). Here we consider the latter, whereas A093738 considers the former. - N. J. A. Sloane, Mar 07 2021

LINKS

Table of n, a(n) for n=1..12.

A. Granville, G. Martin, Prime number races, Amer. Math. Monthly vol 113, no 1 (2006) p 1.

Eric Weisstein's World of Mathematics, Sexy Primes. [The definition in this webpage is unsatisfactory, because it defines a "sexy prime" as a pair of primes.- N. J. A. Sloane, Mar 07 2021].

PROG

(PARI) {c=0; p=7; for(n=1, 9, while(p<10^n, if(isprime(p-6), c++); p=nextprime(p+1)); print1(c, ", "))}

CROSSREFS

Cf. A023201, A046117, A007508, A080840, A006512, A046132, A046117.