Summary: Let $h(n)$ denote the largest product of primes whose sum is $\le n$, and $g(n)$ denote the Landau function, which is the largest product of powers of primes whose sum is $\le n$. In this article, several properties of $h(n)$ are given and compared to similar properties of $g(n)$. Special attention is paid to the behavior of the largest prime factor of $h(n)$.

11A25, 11N37, 11N05, 11-04

distribution of primes, champion number, highly compostite number, Landau function