# Gilbreath's Conjecture

Gilbreath's Conjecture

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

{}

p

n

p

n

{}

d

{1,n}

d

{1,n}

p

n+1

p

n

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

n

k

{}

d

{k,n}

d

{k,n}

d

{k-1,n+1}

d

{k-1,n}

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. )

a

{k}

d

{k,1}

th

1000

d

{k,n}

k

k

min

k

max

n

n

max

k

min

k

max