Partition-theoretic model of prime distribution, II

TL;DR

This paper extends a partition-theoretic deterministic model of prime distribution, providing highly accurate estimates of the prime counting function up to 100,000, based on properties of integer partitions.

Contribution

It introduces a computational model that significantly improves the accuracy of prime count estimates using partition theory, extending previous work to larger n.

Findings

Model estimates for π(n) are almost exact up to n=10,000.

New computational approach improves accuracy up to n=100,000.

Partition properties effectively predict prime distribution.

Abstract

In recent work by Botkin, Dawsey, Hemmer, Just and the present author, a deterministic model of prime number distribution is developed based on properties of integer partitions that gives almost exact estimates for $\pi(n)$, the number of primes less than or equal to positive integer $n$, up to $n=10{,}000$. In this follow-up paper, the author summarizes the ideas behind this partition-theoretic model of primes and formulates a computational model that is practically exact in its estimates of $\pi(n)$ up to $n=100,000$.