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arXiv · 2606.06068

An Elementary Analysis of the Prime Partition Function

Asaf Cohen Antonir·Asaf Shapira
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Abstract

Let $pp (n)$ denote the number of ways to write $n$ as a sum of primes. In this paper, we show that $$ \log pp (n) \sim 2\pi\sqrt{\frac{n}{3\log n}}\;. $$ While sharper estimates are already known, they rely on highly involved and lengthy proofs. In sharp contrast, our approach uses a short, elementary recipe that easily adapts to yield similar asymptotic estimates for several related, extensively studied problems.

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Asaf Cohen Antonir, Asaf Shapira. 2026-06-04. An Elementary Analysis of the Prime Partition Function. https://arxiv.org/abs/2606.06068

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