What is a prime number?

A prime number is a natural number greater than one that has exactly two distinct positive divisors: one and itself. This definition means that a prime number cannot be divided evenly by any other numbers aside from one and the number itself, which ensures that it does not have any additional factors.

For example, the number 5 is prime because it can only be divided evenly by 1 and 5. In contrast, a composite number, which is incorrectly referenced in another option, has more than two divisors and can be factored into smaller positive integers.

Choosing the correct understanding of prime numbers helps in various areas of mathematics, particularly in number theory where primes are fundamental building blocks of the integers, as every integer can be expressed as a product of prime numbers (this is known as the fundamental theorem of arithmetic).

This foundational knowledge is crucial for understanding higher-level concepts in mathematics, including cryptography, algorithms, and more.