What is the current state of understanding, if any, of Gilbreath's Conjecture? (This is that every row after the first begins with a 1 in the following 2 3 5 7 11 13 17 19 23 29 31 ... 1 2 2 4 2 4 2 4 6 2 6 ... 1 0 2 2 2 2 2 2 4 4 2 ... 1 2 0 0 0 0 0 2 0 2 0 ... 1 2 0 0 0 0 2 2 2 2 0 ... 1 2 0 0 0 2 0 0 0 2 0 ... 1 2 0 0 2 2 0 0 2 2 2 ... 1 2 0 2 0 2 0 2 0 0 0 ... 1 2 2 2 2 2 2 2 0 0 0 ... 1 0 0 0 0 0 0 2 0 0 2 ... 1 0 0 0 0 0 2 2 0 2 0 ... ... where the top row is the primes and each lower row the absolute differences of that above it. It has been extensively computationally verified.) This seems MUCH more remarkable than, say, Goldbach's Conjecture!