The Development of Prime Number Theory : From Euclid to Hardy and Littlewood

Władysław Narkiewicz

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 proof of their infinitude, now regarded as canonical. One feels Euclid’s argument has its place in this 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 are still far from their optimal form, and this book aims to present the development of methods with which such problems were attacked over time.

The Development of Prime Number Theory is not a historical book since the author refrains from giving biographical details of the people who have played a role in this development. The author does not discuss the questions concerning why each particular person became in­ interested in primes. His idea is to present the development of the theory of the distribu­tion of prime numbers in the period starting in antiquity and concluding at the end of the first decade of the 20th century.