Researched
Prime Number Theorem
Hadamard and de la Vallée Poussin prove (1896) that primes thin out like 1/ln n, using Riemann's complex zeta function.
Open in the interactive tree →Gauss guessed the law as a teenager, Riemann's 1859 memoir tied primes to the zeros of the zeta function, and the 1896 proofs used complex analysis. The theorem tells us that large primes are plentiful, which public-key cryptography relies on, and it frames the open Riemann Hypothesis.
Prerequisites
Unlocks
- Public-Key Cryptography1976RSA needs large primes; the theorem says they are plentiful
- Riemann HypothesisopenThe Riemann hypothesis would sharpen the prime number theorem
- Primes Fully UnderstoodopenUnderstanding primes fully means improving on the prime number theorem