Divisibility and PrimesThe Riemann Hypothesis

However, as you can see above, there is still a significant error between the actual number of primes, and Gauss’s approximation. In 1859, the mathematician Bernhard Riemann discovered an approximation that looked much better, but he wasn’t able to prove that it would always work. His idea became known as the Riemann Hypothesis.

Hundreds of mathematicians have tried to prove Riemann’s hypothesis, but all without success. It is often considered one of the most difficult and most important unsolved problems in mathematics. In 2000, the Clay Mathematics Institute named it one of seven Millennium Prize Problems and promised $1,000,000 to any mathematician who solves it.