# Frobenius pseudoprime

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Frobenius pseudoprime

In number theory, a Frobenius pseudoprime is a composite number which passes a three-step probable prime test set out by Jon Grantham in section 3 of his paper "Frobenius pseudoprimes". [Jon Grantham. [http://www.pseudoprime.com/pseudo1.pdf Frobenius pseudoprimes] . "Mathematics of Computation", 70 (234): 873-891. 2001.] 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 1/7710, which would require 7 rounds to achieve with the Miller-Rabin primality test according to best known bounds.

References

ee also

*Pseudoprime
*Strong Frobenius pseudoprime
*Ferdinand Georg Frobenius

* [http://www.mathpages.com/home/kmath003/kmath003.htm Symmetric Pseudoprimes] at MathPages

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