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

233, 929, 2089, 5801, 8353, 11369, 18793, 23201, 33409, 39209, 52201, 59393, 67049, 75169, 92801, 112289, 133633, 156833, 169129, 181889, 222953, 284201, 300673, 317609, 335009, 449153, 469801, 490913, 534529, 557033, 580001, 627329, 651689, 891809, 1041449

Offset: 1

Author

Bruno Berselli, Oct 18 2013

Keywords

• nonn

Comments

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

References

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

Links

• Bruno Berselli, Table of n, a(n) for n = 1..1000
• Umberto Cerruti, I numeri idonei di Eulero (in Italian), p. 4.
• Euler Archive, E718 -- Facillima methodus plurimos numeros primos praemagnos inveniendi
• Leonhard Euler, An easy method for finding many very large prime numbers, arXiv:math/0507401 [math.HO], 2005-2008. Translated from Latin.

Crossrefs

Cf. A000926, A230391 (associated n).

Programs

Magma

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

Mathematica

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