A146536 Sum of the first 10^n twin primes.

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

Offset

0,1

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.

Links

Table of n, a(n) for n=0..10.

Cino Hilliard, Counting and summing primes [Dead link]

Kevin Ryde, C Code

Formula

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

Example

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.

Prog

(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

Crossrefs

Cf. A086169, A118552.

Sequence in context: A112578 A112579 A064072 * A189646 A348795 A304018

Adjacent sequences: A146533 A146534 A146535 * A146537 A146538 A146539

Keyword

nonn,more

Author

Cino Hilliard, Oct 31 2008

Extensions

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

Status

approved