## Students Working Seminar in Number Theory

**Date:** February 17, 2020

**Time:** 4:00PM - 5:00PM

**Location:** Bloc605ax

**Speaker:** Erik Davis, Texas A&M University

**Title:** *An Elementary Proof of Bertrand's Postulate*

**Abstract:** In 1845, Bertrand conjectured that for every natural number n beyond 1, there exists a prime between n and 2n. Bertrand was not able to prove this conjecture but had verified the truth of the statement for each n up to 3,000,000. In 1850, Chebyshev proved the result using techniques of complex analysis and a shorter analytic proof was later given by Ramanujan. Despite the simple statement of the theorem, the mathematical community was not successful in finding an elementary proof of the result until 1932, when an 18 year old Paul Erdős deduced the result by observing a few properties of the central binomial. In this talk, I will provide the elementary proof first given by Paul Erdős.