1. People were already interested in prime numbers in ancient times,
and the first result concerning the distribution of primes appears in
Euclid's Elemen- ta, where we find a proof of their infinitude, now
regarded as canonical. One feels that Euclid's argument has its place in
The Book, often quoted by the late Paul ErdOs, where the ultimate forms
of mathematical arguments are preserved. Proofs of most other results on
prime number distribution seem to be still far away from their optimal
form and the aim of this book is to present the development of methods
with which such problems were attacked in the course of time. This is
not a historical book since we refrain from giving biographical details
of the people who have played a role in this development and we do not
discuss the questions concerning why each particular person became in-
terested in primes, because, usually, exact answers to them are
impossible to obtain. Our idea is to present the development of the
theory of the distribu- tion of prime numbers in the period starting in
antiquity and concluding at the end of the first decade of the 20th
century. We shall also present some later developments, mostly in short
comments, although the reader will find certain exceptions to that rule.
The period of the last 80 years was full of new ideas (we mention only
the applications of trigonometrical sums or the advent of various sieve
methods) and certainly demands a separate book.
