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".^[1] 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.

Contents 1 Strong Frobenious pseudoprimes 2 See also 3 References 4 External links

[edit] Strong Frobenious pseudoprimes

A strong Frobenius pseudoprime is a pseudoprime which obeys an additional restriction beyond that required for a Frobenius pseudoprime. ^[2]

[edit] See also

• Pseudoprime
• Ferdinand Georg Frobenius

[edit] References

1. ^ Jon Grantham. Frobenius pseudoprimes. Mathematics of Computation, 70 (234): 873-891. 2001.
2. ^ Weisstein, Eric W., "Strong Frobenius pseudoprime" from MathWorld.

[edit] External links

• Symmetric Pseudoprimes at MathPages

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