Doodling maths: Visualising prime numbers

Prime numbers are a cryptographer’s dream: It’s easy to take two very large prime numbers and multiply them, but it’s extremely hard to do the opposite. There is no fast algorithm (yet) to factorize an integer into its prime factors, if you try to factor a large prime number you’ll have to try every possible number between 2 and that large prime number. This makes primes the ultimate favourites for cryptography.

Because prime numbers have been in the spotlight for a while, there is a growing interest in finding what the next big one is. The record at the moment is 257,885,161 − 1, a number with 17,425,170 digits. Unfortunately (or fortunately for some), there is no easy way of finding primes, no pattern you can follow to predict them. This doesn’t mean people haven’t been trying to crack the mystery for as long as prime numbers have existed, but nobody has yet made it.

However, some of those attempts resulted in beautiful graphs that display a strange, enchanting pseudo-symmetry. Here are some examples. If you find a new one, let us know!

Images source: Ulam Spiral, Wolfram MathWorld, PrimePuzzles, David Cox.

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