A146536 Sum of the first 10^n twin primes.

8, 908, 328184, 69004076, 11556327260, 1707243198956, 237064232862404, 31153163750203064, 3947120494191630260, 486665774050923191336, 58727077924563028184984

Offset: 0

Author

Cino Hilliard, Oct 31 2008

Keywords

• nonn
• more

Comments

The author's Gcc/Gmp program is in the links section. The page also has the PARI bisection algorithms which give a very good approximation for the n-th prime number and the n-th lower twin prime number. The first 5 terms can be computed from the PARI script although 11556327260 takes 4 hours on a 2.53ghz 2 gig ram p4.

Examples

			The 10^0-th twin prime pair is (3,5). This adds up to 8, the first entry in the sequence.
The first 10^1 twin prime pairs are (3,5),(5,7),(11,13) (17,19),(29,31),(41,43),(59,61),(71,73),(101,103),(107,109). This adds up to 908, the second entry in the table.
		

Links

• Cino Hilliard, Counting and summing primes [Dead link]
• Kevin Ryde, C Code

Crossrefs

Cf. A086169, A118552.

Programs

C

// See links.

PARI

a(n)={my(k=10^n,s=k,q); forprime(p=3, oo, if(p==q+2, s+=q; k--; if(!k, return(2*s))); q=p)} \\ Andrew Howroyd, Oct 22 2023

Formula

a(n) = A086169(10^n). - Andrew Howroyd, Oct 22 2023

Extensions

a(10) corrected by Bill McEachen, Oct 16 2023