There are a number of ways to generate primes. One of the oldest is known as the ‘Sieve of Eratosthenes’, named after the Greek mathematician and scholar (who also invented a system of latitude and longitude). Here’s how it works – Starting from the No.2 – the smallest prime – you write down each consecutive number up to your chosen maximum. Now eliminate every multiple of 2; the first number that is missed out from this process will be the next prime – No.3. Now delete each multiple of 3, and repeat. Those left out each time are the primes.

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If you could write an algorithm or program that could predict the next prime from any number, you would soon become the most famous person that ever lived. Riches would follow.