A118552 Sum of the twin prime pairs less than 10^n.

20, 488, 24236, 1726412, 109114568, 7424366648, 545678596592, 41205774636932, 3234489739234676, 260643410442091112, 21446976192435396140, 1795640886305783918948, 152542601906447626814216, 13119246582832293524505360

Offset: 1

Author

Cino Hilliard, May 07 2006

Keywords

• hard
• nonn

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) = 10304185697298. This is an error of 0.00002661. Pi_2(n): Number of twin prime pairs <= n.

Examples

			(3,5),(5,7) are the two twin prime pairs less than 10. These add up to 20, the first term in the sequence.
		

Links

• Cino Hilliard, Sum of twin primes less than 10^n. [Broken link]

Crossrefs

Cf. A007508.

Programs

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","); ) }

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