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This is the Prime Pages'
interface to our BibTeX database. Rather than being an exhaustive database,
it just lists the references we cite on these pages. Please let me know of any errors you notice.References: [ Home  Author index  Key index  Search ]
 Odlyzko93
 A. M. Odlyzko, "Iterated absolute values of differences of consecutive primes," Math. Comp., 61 (1993) 373380. MR 93k:11119
Abstract:
Let d_{0}(n) = p_{n}, the nth prime, for n ≥ 1, and let d_{k+1}(n) =  d_{k}(n)  d_{k}(n+1)  for k ≥ 0, n ≥ 1. A well known conjecture, usually ascribed to Gilbreath but actually due to Proth in the 19th century, says that d_{k}(1) =1 for all k ≥ 1. This paper reports on a computation that verified this conjecture for k ≤ π(10^{13}) ~ 3 × 10^{11}. It also discusses the evidence and the heuristics about this conjecture. It is very likely that similar conjectures are also valid for many other integer sequences.
