The Normal Shape of Prime Numbers

Prime numbers behave with eerie mathematical precision. Although their distribution seems random, the count of distinct prime factors of large numbers follows the classic bell curve used in statistics.

This finding is known as the fundamental theorem of probabilistic number theory. It reveals that nature hides a predictable pattern within the seemingly chaotic sequence of integers. Just as heights or test scores cluster around an average, so too do the prime factors of numbers. It is a stunning bridge between rigid arithmetic and the laws of probability.