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A356727
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Primes of the form 4*k^2 + 84*k + 43.
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0
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43, 131, 227, 331, 443, 563, 691, 827, 971, 1123, 1283, 1451, 1627, 1811, 2003, 2203, 2411, 2851, 3083, 3323, 3571, 4091, 4363, 4643, 4931, 5227, 5531, 5843, 6163, 6491, 6827, 7523, 7883, 8627, 9011, 9403, 9803, 10211, 10627, 11483, 11923, 13291, 13763, 14243, 14731, 15227, 15731
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OFFSET
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1,1
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COMMENTS
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The polynomial 4*k^2 + 84*k + 43 has prime values for k from 0 to 16. The proportion of prime numbers (23.28%) obtained among the first ten million values is slightly higher than that (22.08%) obtained with Euler's polynomial k^2 - k + 41.
The polynomial 4*k^2 + 84*k + 43 produces a Hardy-Littlewood constant of 7.3291180993696....
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LINKS
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MATHEMATICA
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Select[Table[4k^2+84k+43, {k, 0, 60}], PrimeQ] (* Harvey P. Dale, May 07 2023 *)
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CROSSREFS
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KEYWORD
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nonn,less
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AUTHOR
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STATUS
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approved
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