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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.

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    @GerryMyerso$n$ In my defense, "to be strongly estimated" is an attempt to convey the property of significant reduction in the error function for the prime gap, and "exact proof of the nature of primes" is to imply inductive proof of some set of properties of the gap between primes. Your point is duly noted, though; reducing such conveyances to inexact prose loses much of a phrase's exact meaning. Hence the need for a discussion of semantics.2011-11-06

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