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A137475
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Positive numbers k such that k^3 - (k+1)^2 and k^3 + (k+1)^2 are both primes.
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2
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3, 8, 15, 35, 39, 45, 50, 65, 92, 99, 122, 140, 164, 167, 170, 198, 237, 284, 287, 297, 339, 354, 408, 435, 515, 522, 552, 582, 594, 650, 668, 708, 725, 737, 753, 830, 1010, 1068, 1098, 1128, 1253, 1295, 1373, 1424, 1502, 1548, 1553, 1599, 1704, 1779, 1817
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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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3^3 +- 4^2 -> (11, 43) (both primes);
167^3 +- 168^2 = 4657463 +- 28224 -> (4629239, 4685687) (both primes).
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MATHEMATICA
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Select[Range[900], PrimeQ[ #^3-(#+1)^2]&&PrimeQ[ #^3+(#+1)^2]&]
bpQ[n_]:=Module[{a=(n+1)^2}, AllTrue[n^3+{a, -a}, PrimeQ]]; Select[Range[ 2, 2000], bpQ] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Oct 17 2019 *)
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PROG
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(Magma) [n: n in [2..500] | IsPrime(n^3-(n+1)^2)and IsPrime(n^3 +(n+1)^2)] // Vincenzo Librandi, Nov 24 2010
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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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