Edition

This book is dedicated to the memory of Paul Erdos, w

left us in September 1996, at the very moment when

completed the writing of the first edition. He was an

cle to us (and so his friends called him) and a master.

giant of mathematics disappeared: his influence will be

profoundly in the centuries to come.

Number 571 of the collection Que sais-je? already has a histo

The first edition dates from 1953. It was written by Emile Borel

mathematician of great breadth, who profoundly influenced the th

ories of analysis, probability and mathematical physics. Some of

innovative works dealt with applications of probability to numb

theory, though, regrettably, he did not mention them in his mon

graph Les nombres premiers. Using randomness to study certain

may seem somewhat surprising. It is, however, one of the deep

contributions of our century to mathematics in general and to t

theory of numbers in particular.

In 1969, Jean Itard took over from Borel and brought out a n

text, devoting the major part to algebraic methods, which are c

tainly more accessible to a broad audience.