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A230392 Primes of the form 232*m^2+1. 2

%I #31 Sep 08 2022 08:46:06

%S 233,929,2089,5801,8353,11369,18793,23201,33409,39209,52201,59393,

%T 67049,75169,92801,112289,133633,156833,169129,181889,222953,284201,

%U 300673,317609,335009,449153,469801,490913,534529,557033,580001,627329,651689,891809,1041449

%N Primes of the form 232*m^2+1.

%C Nonprime numbers of this form are: 1, 3713, 14849, 28073, 45473, 83753, 102313, 122729, 145001, 195113, 208801, 237569, 252649, 268193, ...

%D Leonhard Euler, Facillima methodus plurimos numeros primos praemagnos inveniendi, Nova Acta Academiae Scientiarum Imperialis Petropolitanae Tomus XIV (1805), Mathematica et Physico-Mathematica.

%H Bruno Berselli, <a href="/A230392/b230392.txt">Table of n, a(n) for n = 1..1000</a>

%H Umberto Cerruti, <a href="/A230392/a230392.pdf">I numeri idonei di Eulero</a> (in Italian), p. 4.

%H Euler Archive, <a href="http://eulerarchive.maa.org/pages/E718.html">E718 -- Facillima methodus plurimos numeros primos praemagnos inveniendi</a>

%H Leonhard Euler, <a href="http://arxiv.org/abs/math/0507401">An easy method for finding many very large prime numbers</a>, arXiv:math/0507401 [math.HO], 2005-2008. Translated from Latin.

%t Select[Table[232 n^2 + 1, {n, 100}], PrimeQ]

%o (Magma) [m: n in [1..100] | IsPrime(m) where m is 232*n^2+1];

%Y Cf. A000926, A230391 (associated n).

%K nonn

%O 1,1

%A _Bruno Berselli_, Oct 18 2013

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Last modified May 4 05:13 EDT 2024. Contains 372227 sequences. (Running on oeis4.)