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# Physical Mathematics

ISSN: 2090-0902

Open Access

## The Proof of the Infinity of Twin Primes

### Abstract

Yoichiro Hosoya

This paper shows that there are infinitely many twin primes through a focused analysis of twin primes whose last digits are 1 and 3. As a method, the original Infinite Game and Floor Line Arrangement are added to the refined one of Sieve of Eratosthenes. In the first section, we describe the extraction of twin prime numbers by the Sieve of Eratosthenes from the combination of natural numbers whose last digits are 1 and 3 and the numbers differ by 2. If such a twin prime number is finite, from some point all numbers are marked. In the second section, we use the Infinite Game, but what we do here is the same as the Sieve of Eratosthenes above, except for one point. The only exception is that we can choose where to mark regardless of the prime number. In the third section, we show that it is impossible to mark all numbers even when we artificially select a place to mark in the Infinite Game, by using the method of the Floor Line Arrangement. In the fourth section, we conclude that as a result, it is revealed that there are infinitely many twin prime numbers.