# Talk:Frobenius pseudoprime

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Field:  Number theory

## Merger proposal

This article and strong Frobenius pseudoprime are closely related and the latter is very thin. I propose to merge them. Richard Pinch (talk) 20:22, 20 August 2008 (UTC)

merged phoebe / (talk to me) 01:09, 2 November 2008 (UTC)

## explains nothing

This article does not define what a Frobenius pseudoprime is at all. For example, reading this article does not help in any way to check the claimed result that 4181 is an example.--Hagman (talk) 15:10, 16 October 2013 (UTC)

A definition is given on page 9 in the first reference at http://mathworld.wolfram.com/FrobeniusPseudoprime.html. It reads:
A Frobenius pseudoprime with respect to a monic polynomial f(x) is a composite which is a Frobenius probable prime with respect to f(x).
Perhaps that definition should be added to the article. It should be noted that the exact definition depends on the parameters chosen for the quadratic Frobenius test. -- Toshio Yamaguchi 15:52, 16 October 2013 (UTC)

## The first Frobenius pseudoprime to x^2-3x-1

649, 4187, 12871, 14041, 23479, 24769, 28421, 34997, 38503, 41441, 48577, 50545, 58081, 59081, 61447, 95761, 96139, 116821, 127937, 146329, 150281, 157693, 170039, 180517, 188501, 281017, 321441, 349441, 363091, 397927, 423721, 440833, 473801, 478401, 479119, 493697, 507529, 545273, 550551, 558145, 561601, 587861, 597871, 625049, 665473, 711361, 712481, 749057, 841753, 842401, 860161, 888445, 930151, 979473, 1019041, 1034881, 1115687, 1152271, 1153741, 1184401, 1241633, 1252033, 1270801, 1351633, 1361837, 1373633, 1374649, 1477909, 1493857, 1531531, 1548481, 1553473, 1578977, 1596403, 1599329, 1699201, 1703677, 1755001, 1758121, 1822285, 1854841, 1879809, 1920985, 1987021, 2030341, 2132737, 2250767, 2260021, 2288209, 2290289, 2320501, 2480689, 2508013, 2525563, 2538251, 2590981, 2639329, 2908181, 2931673, 2984983, 3024505, 3057601, 3141841, 3362083, 3383353, 3384001, 3385041, 3575121, 3581761, 3629857, 3717419, 4082653, 4137251, 4224533, 4231681, 4335241, 4411837, 4555651, 4682833, 4835377, 4972033, 5000449, 5002013, 5160013, 5252101, 5263553, 5419751, 5430643, 5434153, 5604161, ... — Preceding unsigned comment added by 101.14.112.72 (talk) 14:38, 14 March 2015 (UTC)

## Is 58081 a Frobenius pseudoprime to x^2-3x-1 ?

According to the Quadratic Frobenius test article, if sqrt(n) is an integer, then it return composite immediately, and sqrt(58081) is an integer, so 58081 should not be a Frobenius pseudoprime. — Preceding unsigned comment added by 101.8.115.219 (talk) 16:19, 13 August 2015 (UTC)

The QFT is a different test, and should not be confused with the Frobenius test with respect to a quadratic polynomial. It adds numerous extra conditions on top of the Frobenius criteria. The naming is unfortunate. I don't see anything about a perfect square test of n in either this article's description or in his paper. It's an interesting point though, as these tests aren't uncommon. DAJ NT (talk) 19:57, 18 August 2015 (UTC)