Edouard Lucas and Primality Testing

Describes the development and extension of fundamental idea of Edouard Lucas, a French mathematician and mathematical recreationist, that is still used today in the verification of the largest primes. Preliminaries.

The Beginnings.

Lucas' Early Work.

The Lucas Functions.

Lucas' Tests.

Later Developments.

Early Devices.

Kraitchik and Lehmer.

Finite Fields.

Lucas's Functions Generalized.

Special Tests for Primality.

The Influence of the Computer.

Results from the Computer.

Primality Proofs.

Probabilistic Primality Tests.

Recent Sieve Devices.

Primality Proving Today.

Bibliography.

Index.

Hugh Cowie Williams is a Canadian mathematician. He deals with number theory and cryptography.