The Density of Prime Numbers - A Mathematical Proof

Explore a 39-minute mathematics video that presents an elementary proof demonstrating how prime numbers become increasingly sparse, without relying on the Prime Number Theorem. Learn about the theorem's key consequences, including the infinitude of primes and the zero density of prime numbers, through a detailed examination of the prime counting function. Delve into fundamental mathematical concepts including sets, subsets, binomial coefficients, and logarithms while following a structured proof originally developed by Idris D. Mercer. Progress through six detailed proof segments that systematically establish how the density of prime numbers approaches zero as numbers increase towards infinity.