Understanding Prime Distributions
Prime numbers have fascinated mathematicians for millennia. While the sequence of primes appears irregular, deep patterns emerge when we examine their distribution.
The Prime Number Theorem
The Prime Number Theorem (PNT) describes the asymptotic density of primes. It states that the number of primes less than a large number n is approximately n / ln(n). This means primes become sparser, but they never disappear.
Visualizing Gaps Between Primes
One way to explore the distribution is by looking at the gaps between consecutive primes. The chart below plots the average gap size for intervals of 1,000 numbers up to 100,000.