# On a conjecture of B. C. Kellner

## TL;DR

This paper proves a recent conjecture by Kellner regarding the number of distinct prime factors in a specific prime product, utilizing advanced analytic number theory techniques.

## Contribution

It provides a rigorous proof of Kellner's conjecture using sophisticated estimates from analytic number theory.

## Key findings

- Confirmed Kellner's conjecture on prime factors
- Applied Granville-Ramaré exponential sum estimates
- Enhanced understanding of prime factorization in special products

## Abstract

The aim of this note is a proof of a recent conjecture of Kellner concerning the number of distinct prime factors of a particular product of primes. The proof uses profound results from analytic number theory, such as Granville-Ramar\'{e}'s estimate of an exponential sum over primes.