Search: id:A118552
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%I A118552
%S A118552 20,488,24236,1726412,109114568,7424366648,545678596592,41205774636932,
%T A118552 3234489739234676,260643410442091112,21446976192435396140,
%U A118552 1795640886305783918948,152542601906447626814216,13119246582832293524505360
%N A118552 Sum of the twin prime pairs less than 10^n.
%C A118552 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 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). Eg., Sum of twin primes 
               <= 10^8 divided by 4 = 10301443659233. Pi_2(10^16) = 10304185697298. 
               This is an error of .00002661.
%H A118552 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>.
%F A118552 Pi_2(n): Number of twin prime pairs <= n.
%e A118552 (3,5),(5,7) are the two twin prime pairs less than 10. These add up to 
               20, the
%e A118552 first term in the sequence.
%o A118552 (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 A118552 Sequence in context: A065412 A159753 A000827 this_sequence A092087 A008270 
               A130186
%Y A118552 Adjacent sequences: A118549 A118550 A118551 this_sequence A118553 A118554 
               A118555
%K A118552 hard,nonn
%O A118552 1,1
%A A118552 Cino Hilliard (hillcino368(AT)gmail.com), May 07 2006
%E A118552 2 more terms from Giovanni Resta (g.resta(AT)iit.cnr.it), May 08 2006
%E A118552 Added a(13) and a(14).Added to the comment. Changed the link to a better 
               program.Edited the example. - Cino Hilliard (hillcino368(AT)hotmail.com), 
               Nov 18 2008

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