Prime Number Theorem

The Prime Number Theorem describes how prime numbers—those greater than 1 that can only be divided by 1 and themselves—are distributed among the whole numbers. It states that as numbers get larger, the average distance between consecutive prime numbers increases and is approximately related to the natural logarithm of the numbers. Specifically, it suggests that the number of primes less than a given number \( n \) is roughly \( n / \log(n) \). This helps mathematicians understand the frequency and distribution of prime numbers in the vast landscape of integers.