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A118552
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Sum of the twin prime pairs less than 10^n.
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3
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20, 488, 24236, 1726412, 109114568, 7424366648, 545678596592, 41205774636932, 3234489739234676, 260643410442091112, 21446976192435396140, 1795640886305783918948, 152542601906447626814216, 13119246582832293524505360
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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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 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.
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LINKS
| Cino Hilliard, Sum of twin primes less than 10^n.
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FORMULA
| Pi_2(n): Number of twin prime pairs <= n.
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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.
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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", "); ) }
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CROSSREFS
| Sequence in context: A065412 A159753 A000827 * A092087 A008270 A130186
Adjacent sequences: A118549 A118550 A118551 * A118553 A118554 A118555
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KEYWORD
| hard,nonn
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AUTHOR
| Cino Hilliard (hillcino368(AT)gmail.com), May 07 2006
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EXTENSIONS
| 2 more terms from Giovanni Resta (g.resta(AT)iit.cnr.it), May 08 2006
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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