The debate over whether 1 is classified as a prime number centers around its impact on mathematical theorems and proofs. Excluding 1 maintains the clarity and elegance of theorems like the fundamental theorem of arithmetic, which asserts that every positive integer can be expressed uniquely as a product of prime numbers, provided that prime numbers are greater than 1. If 1 were considered prime, it would complicate this theorem and lead to unnecessary repetition in statements, ultimately reducing the aesthetic and formal quality of mathematical discourse. Furthermore, similar debates arise in foundational areas of mathematics, such as whether 0 should be categorized as a natural number, pointing to broader discussions within mathematics about definitions and their implications.