As an information theoretician, it's a personal hobby of mine to find elegant analogies to open mathematical problems. After all, they have a profound impact on how I conduct my research and how I secure my systems from theoretical attacks.
While playing with Gilbreath's conjecture, I noticed, as many do, that the conjecture might be solved trivially if one could reason exactly about an infinite sequence of prime numbers. Because all other aspects of the problem are known (including the properties of the forward difference function) and because proof of the Riemann hypothesis can be reasoned to be hypothetically as difficult as a solution to the conjecture (through the nature of prime numbers), can a variation of Gilbreath's conjecture be shown to be solved inductively by application of the Riemann zeta function? If so, what implications does this have?
I'm probably well off base here, and this property is probably well known. But, my curiosity is insatiable. Links to supporting information or other questions may well be sufficient to answer this conjecture.