A Possible Solution for Hilbert's Unsolved 8th Problem: Twin Prime Conjecture

TL;DR

This paper claims to provide a proof for the Twin Prime Conjecture by analyzing prime pairs within a specific range and demonstrating the existence of infinitely many twin primes.

Contribution

It presents a novel approach to prove the Twin Prime Conjecture, asserting the existence of infinitely many twin prime pairs.

Findings

At least three additional twin prime pairs found as n increases.

Twin prime pairs increase within the specified range.

Claimed proof of the Twin Prime Conjecture.

Abstract

We measure whether there are numerous pairs of twin primes (hereafter referred to as twin prime pairs) according to the prime number inferred by sieve of Eratosthenes. In this study, we reveal at least three additional twin prime pairs increased as n is increased by 1, while setting (6n+5)**2 as the range for estimating twin prime pairs. As a result, we prove the Twin Prime Conjecture proposed by de Polignac in 1849. That is, there are numerous twin prime pairs, indicating that there are numerous prime number p for each natural number k by making p + 2k as prime number for the case of k = 1.