Frobenius Tests

Grantham introduced Frobenius pseudoprimes as an overarching approach to probable prime testing in the context of finite fields. Since his second paper on the subject about quadratic Frobenius tests there have been many such tests devised. Most of these define a test with some root finding over the structures, use random bases and give error bounds.

Grantham: A Probable Prime Test with High Confidence (RQFT)

Müller: A Probable Prime Test with Very High Confidence for n equiv 1 mod 4

Damgård & Frandsen: An extended quadratic Frobenius primality test with average and worst case error estimates (EQFT)

Seysen: A Simplified Quadratic Frobenius Primality Test (SQFT)

Khashin: Counterexamples for Frobenius primality test

Underwood: Quadratic Frobenius probable prime tests costing two selfridges

Wiki page: Frobenius pseudoprime