Infinite Primes From Integer Partitions

Abstract

Ferrers diagrams are used to visually represent integer partitions. We describe a way to use Ferrers diagrams to uniquely represent integers in terms of their prime factors. This leads to a lower bound on the number of primes less than a given integer, namely $\ddot{I}€(x)\ge \frac{\lfloor \lg x\rfloor }{\lg (\lfloor \lg x\rfloor +1)}$ where $\ddot{I}€(x)$ is the prime counting function and $\lg (x)$ denotes the base 2 logarithm. This results in a new proof of the infinitude of primes.

5 pages, 2 figures