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A139677
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Estimate of the sum of twin prime pairs < 10^n = 4*Pi2(10^2n).
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OFFSET
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1,1
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COMMENTS
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Since we have SumTP(n) up to n=10^12, we can reverse this process and estimate Pi2(n) for n = 18,20,22,24. Since 4*Pi2(2n) ~ SumTP(n), Pi2(2n) ~ SumTP(n)/4.
The link shows these estimates and the relative error. Also estimated is the odd values 17,19,21,23,25 by curve fitting 6 points to a 5th degree polynomial to the base-10 log of the values and interpolating.
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LINKS
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FORMULA
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Pi2(n) is the twin prime counting function = number of twin prime pairs < n. a(n) = 4*A007508(2n) for n <= 8. SumTP(n) = sum of twin prime pairs < n.
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EXAMPLE
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For n = 8, SumTP(8) = A118552(8) = 41205774636932. Pi2(16)= 10304185697298.
4*Pi2(16) = 41216742789192. This has an error of 0.00026...
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CROSSREFS
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KEYWORD
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nonn,more
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AUTHOR
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STATUS
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approved
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