
Elementary
Facts
About
the
Distribution
of
Primes
Title: 
Elementary Facts About the Distribution of Primes 
Author:

Manuel Eberl

Submission date: 
20190221 
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). 
BibTeX: 
@article{Prime_Distribution_ElementaryAFP,
author = {Manuel Eberl},
title = {Elementary Facts About the Distribution of Primes},
journal = {Archive of Formal Proofs},
month = feb,
year = 2019,
note = {\url{https://isaafp.org/entries/Prime_Distribution_Elementary.html},
Formal proof development},
ISSN = {2150914x},
}

License: 
BSD License 
Depends on: 
Prime_Number_Theorem, Zeta_Function 
Used by: 
IMO2019, Irrational_Series_Erdos_Straus, Zeta_3_Irrational 
Status: [ok] 
This is a development version of this entry. It might change over time
and is not stable. Please refer to release versions for citations.

