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A230391
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Numbers m such that 232*m^2+1 is prime.
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2
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1, 2, 3, 5, 6, 7, 9, 10, 12, 13, 15, 16, 17, 18, 20, 22, 24, 26, 27, 28, 31, 35, 36, 37, 38, 44, 45, 46, 48, 49, 50, 52, 53, 62, 67, 71, 72, 73, 74, 76, 79, 81, 82, 86, 87, 94, 95, 99, 100, 104, 106, 107, 112, 113, 115, 118, 119, 121, 124, 126, 127, 136, 138
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OFFSET
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1,2
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COMMENTS
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The form "232aa + 1" has been used by Euler to find idoneal numbers (A000926), and 232 itself is an idoneal number (see References).
Numbers m for which 232*m^2+1 is not prime are: 0, 4, 8, 11, 14, 19, 21, 23, 25, 29, 30, 32, 33, 34, 39, 40, 41, 42, 43, 47, ... (see table on page 14 of Euler's paper).
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REFERENCES
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Leonhard Euler, Facillima methodus plurimos numeros primos praemagnos inveniendi, Nova Acta Academiae Scientiarum Imperialis Petropolitanae Tomus XIV (1805), Mathematica et Physico-Mathematica (this sequence is on page 10).
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LINKS
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MATHEMATICA
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Select[Range[200], PrimeQ[232 #^2 + 1] &]
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PROG
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(Magma) [n: n in [1..200] | IsPrime(232*n^2+1)];
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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