A surprising conjecture about the gaps between primes, namely: Let denote the ordered sequence of prime numbers , and define each term in the sequence by

,

where is positive. Also, for each integer greater than 1, let the terms in be given by

.

Gilbreath's conjecture states that every term in the sequence is 1. With this Demonstration you can check this amazing statement up to the difference series. The controls let you see the matrix of , where goes from to , and goes from 1 to . (If , they switch roles. )