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A139780
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Average of twin primes of the form p1^3 + p2^2, where p1 < p2 are twin primes.
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4
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38318210940, 68484878220, 143165125680, 6353554336290, 75041090138100, 91851874324800, 116366750976990, 118525130067690, 368776631152800, 374826155288910, 431041855258500, 585102141663000, 767853933976740, 834602006112360, 845499208101600, 1560061877051100
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OFFSET
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1,1
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LINKS
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EXAMPLE
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38318210940 = 3371^3 + 3373^2 is a term since both (3371, 3373) and (38318210939, 38318210941) are twin primes.
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MATHEMATICA
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a={}; Do[p1=Prime[n]; p2=Prime[n+1]; pp=p1^3+p2^2; If[(p2-p1)==2&&PrimeQ[pp-1]&&PrimeQ[pp+1], AppendTo[a, pp]], {n, 10^4}]; Print[a];
Select[#[[1]]^3+#[[2]]^2&/@Select[Partition[Prime[Range[15000]], 2, 1], #[[2]] - #[[1]]==2&], AllTrue[#+{1, -1}, PrimeQ]&] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Jul 01 2021 *)
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PROG
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(Magma) [q:k in [1..10000]|IsPrime((NthPrime(k)+2)) and IsPrime(q-1)and IsPrime(q+1) where q is NthPrime(k)^3+ (NthPrime(k)+2)^2]; // Marius A. Burtea, Dec 22 2019
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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