

A230391


Numbers m such that 232*m^2+1 is prime.


2



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

1,2


COMMENTS

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).


REFERENCES

Leonhard Euler, Facillima methodus plurimos numeros primos praemagnos inveniendi, Nova Acta Academiae Scientiarum Imperialis Petropolitanae Tomus XIV (1805), Mathematica et PhysicoMathematica (this sequence is on page 10).


LINKS



MATHEMATICA

Select[Range[200], PrimeQ[232 #^2 + 1] &]


PROG

(Magma) [n: n in [1..200]  IsPrime(232*n^2+1)];


CROSSREFS



KEYWORD

nonn,easy


AUTHOR



STATUS

approved



