Most people have heard of the Sieve of Erathosthenes: put all positive integers in a list, and delete the number one. Now mark two as prime and delete all multi

Most people have heard of the Sieve of Erathosthenes: put all positive integers in a list, and delete the number one. Now mark two as prime and delete all multiples of two. Now mark the next remaining number prime and delete all multiples of that number. Proceed ad infinitum. There's a randomised counterpart to the Sieve of Erathosthenes called the Hawkins ransom sieve: Delete the number 1. Mark two as prime, and delete all the larger integers with probability 1/2. Now mark the smallest remaining integer (n, say) prime, and delete all the remaining larger integers with probability 1/n. Proceed ad infinitum. One of my favourite results in mathematics is that the Riemann hypothesis (i.e. the error bound for the prime number theorem) holds for the Hawkins random primes with probability 1. The proof is only about five pages: https://eudml.org/doc/89234 https://eudml.org/doc/89234