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A118552 Sum of the twin prime pairs less than 10^n. 3


%S 20,488,24236,1726412,109114568,7424366648,545678596592,

%T 41205774636932,3234489739234676,260643410442091112,

%U 21446976192435396140,1795640886305783918948,152542601906447626814216,13119246582832293524505360

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

%C 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.

%H Cino Hilliard, <a href="http://groups.google.com/group/sumprimes/web/sum-of-twin-primes--n">Sum of twin primes less than 10^n</a>. [Broken link]

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

%o (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","); ) }

%Y Cf. A007508.

%K hard,nonn

%O 1,1

%A _Cino Hilliard_, May 07 2006

%E 2 more terms from _Giovanni Resta_, May 08 2006

%E a(13) and a(14) added, comment expanded, program at link improved, and example edited by _Cino Hilliard_, Nov 18 2008

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Last modified August 9 21:08 EDT 2022. Contains 356026 sequences. (Running on oeis4.)