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

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

Offset: 1

Author

Bruno Berselli, Oct 18 2013

Keywords

• nonn
• easy

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 Physico-Mathematica (this sequence is on page 10).

Links

• Bruno Berselli, Table of n, a(n) for n = 1..1000
• Umberto Cerruti, I numeri idonei di Eulero (in Italian), p. 3.
• Leonhard Euler, An easy method for finding many very large prime numbers, p. 8, arXiv:math/0507401 [math.HO], 2005-2008. Translated from Latin.

Crossrefs

Cf. A000926, A230392 (associated primes).

Programs

Magma

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

Mathematica

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

PARI

is(n)=isprime(232*n^2+1) \\ Charles R Greathouse IV, Jun 06 2017