2023/11/06 by Shakov, Anton
#11A51 #FOS: Mathematics #General Mathematics (math.GM)
paper · doi:10.48550/arxiv.2311.03322
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 π(x) ≥ (\lfloor \lg x \rfloor)/(\lg (\lfloor \lg x \rfloor + 1)) where π(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.