Elementary Facts About the Distribution of Primes

Manuel Eberl 🌐

February 21, 2019

This is a development version of this entry. It might change over time and is not stable. Please refer to release versions for citations.

Abstract

This entry is a formalisation of Chapter 4 (and parts of Chapter 3) of Apostol's Introduction to Analytic Number Theory. The main topics that are addressed are properties of the distribution of prime numbers that can be shown in an elementary way (i. e. without the Prime Number Theorem), the various equivalent forms of the PNT (which imply each other in elementary ways), and consequences that follow from the PNT in elementary ways. The latter include, most notably, asymptotic bounds for the number of distinct prime factors of n, the divisor function d(n), Euler's totient function φ(n), and lcm(1,…,n).

License

BSD License

Topics

Session Prime_Distribution_Elementary