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

Offset: 1

Author

Jason Earls, Mar 28 2003

Keywords

• nonn

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

• 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].

Crossrefs

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

See also A031924, A093738.

Programs

PARI

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

Extensions

a(8) and a(9) from Klaus Brockhaus, Mar 30 2003

More terms from R. J. Mathar, Aug 05 2007