Prime Number Theorem

The density of primes thins as the natural logarithm: primes near n occur about one in ln n integers.

Specifications & Metrics

proved

Hadamard and de la Vallée Poussin, 1896

Core Principles & Analysis

• Both 1896 proofs built on Riemann's 1859 zeta-function memoir.
• It answered Gauss, who conjectured the law from teenage prime tables.
• The error term in the theorem is exactly as good as our knowledge of the Riemann hypothesis.