## 1859 – Riemann hypothesis

The Riemann hypothesis is named after Bernhard Riemann, who worked on a technique to predict the distribution of prime numbers. Mersenne and Fermat worked on formulas that can predict *some* prime numbers but not all of them. In 1737 Euler followed up on their work, eventually showing that the summation series of the reciprocals of prime numbers is divergent and therefore the number of primes is infinite. The key function he used in this process is now known as the “zeta function”.

Legendre and Gauss worked on the same problem using a log function and produced the “Prime Number Theorem” which says that for large numbers the density of prime numbers nearby is 1/log(n). Riemann then expanded the zeta function to include complex numbers (numbers with both a real and imaginary part) and made a conjecture about the distribution of zeros. This is known as the Riemann Hypothesis.

1826 – Riemann
1859 – “On the Number of Primes Less Than a Given Magnitude” – Riemann