Iterated absolute values of differences of consecutive primes
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- by Andrew M. Odlyzko PDF
- Math. Comp. 61 (1993), 373-380 Request permission
Abstract:
Let ${d_0}(n) = {p_n}$, the nth prime, for $n \geq 1$, and let ${d_{k + 1}}(n) = |{d_k}(n) - {d_k}(n + 1)|$ for $k \geq 0,n \geq 1$. 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 $k \geq 1$. This paper reports on a computation that verified this conjecture for $k \leq \pi ({10^{13}}) \approx 3 \times {10^{11}}$. 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.References
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Additional Information
- © Copyright 1993 American Mathematical Society
- Journal: Math. Comp. 61 (1993), 373-380
- MSC: Primary 11Y35; Secondary 11N05
- DOI: https://doi.org/10.1090/S0025-5718-1993-1182247-7
- MathSciNet review: 1182247