# Frobenius pseudoprime

In number theory, a Frobenius pseudoprime is a pseudoprime that passes a three-step probable prime test set out by Jon Grantham in 1996.[1][2]

## Example

Frobenius pseudoprimes with respect to polynomial $x^2-x-1$ form a sequence:

4181, 5777, 6721, 10877, 13201, 15251, 34561, 51841, 64079, ... (sequence A212424 in OEIS)

## Properties

Although a single round of Frobenius is slower than a single round of most standard tests, it has the advantage of a much smaller worst-case per-round error bound of $\tfrac{1}{7710}$,[1] which would require 7 rounds to achieve with the Miller–Rabin primality test according to best known bounds.

## Strong Frobenius pseudoprimes

A strong Frobenius pseudoprime is a pseudoprime which obeys an additional restriction beyond that required for a Frobenius pseudoprime.[3]