Divisibility and PrimesDistribution of the Primes

The Riemann Hypothesis

Mathematicians have spent many centuries exploring the pattern and distribution of prime numbers. They seem to appear completely randomly – sometimes there are huge gaps in between consecutive primes, and sometimes we find twin primes

When only 15 years old, the German mathematician Carl Friedrich Gauss

Carl Friedrich Gauss (1777 – 1855) was arguably the greatest mathematician in history. He made groundbreaking discoveries in just about every field of mathematics, from algebra and number theory to statistics, calculus, geometry, geology and astronomy.

According to legend, he corrected a mistake in his father‘s accounting at the age of 3, and found a way to quickly add up all integers from 1 to 100 at the age of 8. He made his first important discoveries while still a teenager, and later tutored many other famous mathematicians as Professor.

Timeline

Along the x-axis you can see all integers. Whenever there is a prime, the Prime Counting Function (shown in blue) increases by one. As we zoom out, the blue line becomes very smooth. Gauss noticed that the shape of this function looks very similar to the function xlogx (shown in red). He predicted that the two functions are always “approximately similar”, and this was proven in 1896.