p-Adic Metrics and the Infinitude of Primes

摘要

By applying a geometric approach, we provide a proof of the infinitude of primes via p-adic metrics. This is a novel approach to a well-known, and quite old, result. There are many proofs for the infinitude of primes, and it is commonly believed that the first one dates back to the ancient Greek mathematician Euclid. All proofs for the infinitude of primes use the fact that prime numbers form a multiplicative basis for the integers, and we will use this in our proof as well. In our approach, we apply p-adic metrics as a novelty.