Primes of the form $p=1+n!\sum n,$ for some $n\in\mathbb{N}^{+}$

TL;DR

This paper reports the discovery of prime numbers of a specific form involving factorials and sums, highlighting a new pattern in prime distribution related to factorial-based expressions.

Contribution

It introduces a novel class of primes defined by the formula p=1+n!∑n, expanding understanding of prime forms and their properties.

Findings

Identification of primes of the form p=1+n!∑n for some n>0

Approximate digit length of these primes correlates with the logarithm of the expression

Provides initial data on the distribution of such primes

Abstract

The purpose of this note is to report on the discovery of the primes of the form $p=1+n!\sum n$, for some natural numbers $n>0$. The number of digits in the prime p are approximately equal to $\lfloor log_{10}(1+n!\sum n)\rceil+1$.