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