Iterated absolute values of differences of consecutive primes

Author:
Andrew M. Odlyzko

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

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Abstract | References | Similar Articles | Additional Information

Abstract: Let , the *n*th prime, for , and let for . A well-known conjecture, usually ascribed to Gilbreath but actually due to Proth in the 19th century, says that for all . This paper reports on a computation that verified this conjecture for . 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.

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DOI:
https://doi.org/10.1090/S0025-5718-1993-1182247-7

Article copyright:
© Copyright 1993
American Mathematical Society