Maximal product of primes whose sum is bounded

TL;DR

This paper investigates the function h(n), which finds the maximum product of distinct primes with a sum not exceeding n, providing properties and an algorithm for large n.

Contribution

The paper introduces new properties of h(n) and presents an efficient algorithm to compute it for large n.

Findings

Characterization of h(n) properties

Algorithm for computing h(n) efficiently

Application to large n values

Abstract

If n is a positive integer, let h(n) denote the maximal value of the product of distinct primes whose sum does not exceed n. We give some properties of this function h and describe an algorithm able to compute h(n) for large values of n.