Gilbreath’s conjecture: a Cramér random model and a deterministic analysis

Zachary Chase, Zach Hunter and I have uploaded to the arXiv our preprint Gilbreath’s conjecture: a Cramér random model and a deterministic analysis. This paper is motivated by a notorious conjecture of Gilbreath (also proposed eighty years prior by Proth), which one can state as follows: if one starts with the sequence of primes and repeatedly takes absolute differences of consecutive terms, then the first term of each subsequent row is always : Coming from a PDE background, I like to think of this conjecture as a (discrete) nonlinear “wave equation” problem, where the primes are the “initial data”, the downward direction in the above pyramid is the arrow of “time”, and the “equation of motion” is that the value of the “scalar field” at any given point in “spacetime” is the absolute difference of the values of the two points directly above it. We will informally refer to solutions to such an “equation” as “Gilbreath arrays”. Numerically, the conjecture has been verified for the first…