Small (~10): The Sieve of Eratosthenes finds primes and also does a decent job demonstrating the “pattern” that they form. If you mark every multiple of 2, you’ll be marking only composite numbers. Turns out that if n isn’t prime, then neither is M n . Create the sequence of numbers, S k , defined recursively as S k = (S k-1 )2 – 2 with S 0 = 4. Answer Gravy: Fermat’s little theorem is pretty easy to use, but it helps to see an example.

When you want to outsmart the world, you turn to the facts. And the facts are in the science.