OFFSET
1,1
COMMENTS
The PARI program can compute the first 9 terms in reasonable time. a(10) was computed by the program in the link. This took 145 sec on a p4 2.53 GHz processor while a(13) took 1.4 days and a(14) took 15 days with multitasking. The sum of twin primes < 10^n divided by 4 gives a very good approximation for the number of twin primes < 10^(2n). E.g., sum of twin primes <= 10^8 divided by 4 = 10301443659233. Pi_2(10^16) = 10304195697298. This is an error of 0.0002671. Pi_2(n): Number of twin prime pairs <= n.
LINKS
Benjamin Chaffin, Table of n, a(n) for n = 1..19
Cino Hilliard, Sum of twin primes less than 10^n. [Broken link]
EXAMPLE
(3,5),(5,7) are the two twin prime pairs less than 10. These add up to 20, the first term in the sequence.
PROG
(PARI) sumtwins(n) = { local(x, j, s, sr, p10x); for(x=1, n, s=0; p10x=10^x; forstep(j=3, 10^x, 2, if(j+2 < p10x && ispseudoprime(j) && ispseudoprime(j+2), s+=j+j+2); ); print1(s", "); ) }
CROSSREFS
KEYWORD
hard,nonn,changed
AUTHOR
Cino Hilliard, May 07 2006
EXTENSIONS
2 more terms from Giovanni Resta, May 08 2006
a(13) and a(14) added, comment expanded, program at link improved, and example edited by Cino Hilliard, Nov 18 2008
a(13) and a(14) corrected by and a(15) onward from Benjamin Chaffin, Jun 02 2026
STATUS
approved