# Improving the Estimates for a Sequence Involving Prime Numbers

## TL;DR

This paper refines estimates for a sequence involving prime numbers using new explicit bounds for the prime counting function, enhancing accuracy in prime-related calculations.

## Contribution

It introduces improved explicit estimates for the sequence C_n based on recent advances in prime counting function bounds.

## Key findings

- Sharper bounds for the sequence C_n involving primes
- Enhanced accuracy in prime number sequence estimates
- Application of new explicit prime counting estimates

## Abstract

Based on new explicit estimates for the prime counting function, we improve the currently known estimates for the particular sequence $C_n = np_n - \sum_{k \leq n}p_k$, $n \geq 1$, involving the prime numbers.