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A230391 Numbers m such that 232*m^2+1 is prime.

%I A230391 #38 Sep 08 2022 08:46:06
%S A230391 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,
%T A230391 44,45,46,48,49,50,52,53,62,67,71,72,73,74,76,79,81,82,86,87,94,95,99,
%U A230391 100,104,106,107,112,113,115,118,119,121,124,126,127,136,138
%N A230391 Numbers m such that 232*m^2+1 is prime.
%C A230391 The form "232aa + 1" has been used by Euler to find idoneal numbers (A000926), and 232 itself is an idoneal number (see References).
%C A230391 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).
%D A230391 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).
%H A230391 Bruno Berselli, <a href="/A230391/b230391.txt">Table of n, a(n) for n = 1..1000</a>
%H A230391 Umberto Cerruti, <a href="/A230391/a230391.pdf">I numeri idonei di Eulero</a> (in Italian), p. 3.
%H A230391 Leonhard Euler, <a href="http://arxiv.org/abs/math/0507401">An easy method for finding many very large prime numbers</a>, p. 8, arXiv:math/0507401 [math.HO], 2005-2008. Translated from Latin.
%t A230391 Select[Range[200], PrimeQ[232 #^2 + 1] &]
%o A230391 (Magma) [n: n in [1..200] | IsPrime(232*n^2+1)];
%o A230391 (PARI) is(n)=isprime(232*n^2+1) \\ _Charles R Greathouse IV_, Jun 06 2017
%Y A230391 Cf. A000926, A230392 (associated primes).
%K A230391 nonn,easy
%O A230391 1,2
%A A230391 _Bruno Berselli_, Oct 18 2013