Gilbreath's conjecture, in number theory, concerns the sequences generated by repeatedly applying the forward difference operator to consecutive prime numbers and taking the unsigned results. It is named after Norman L. Gilbreath, who presented it in 1958 after noticing the pattern by chance while doing arithmetic on a napkin, though the French mathematician Francois Proth had published the same observation in 1878. This description is adapted from Wikipedia contributors under CC BY-SA 4.0; changes were made. https://creativecommons.org/licenses/by-sa/4.0/
Facts
StatementRepeatedly applying the forward difference operator to consecutive primes and taking absolute values, the first term of every resulting sequence is 1. 1 Proposed Year Progress Toward ResolutionOpen; Odlyzko verified it in 1993 for k up to 3.4e11, and later computations extended the verified range of primes. 1 Classification
Resolution Status Prize Status
Prize Status (category) Connections
In Branch
Source Gilbreath's Conjecture (Wikipedia)
Sources
1. Gilbreath's Conjecture (Wikipedia)
Wikimedia FoundationLead section
named after Norman L. Gilbreath who, in 1958, presented it to the mathematical community
Lead section, first sentence
regarding the sequences generated by applying the forward difference operator to consecutive prime numbers and leaving the results unsigned
Verification and attempted proofs
The conjecture remains an open problem.
In Branch: Number Theory, Lead sentence
Gilbreath's conjecture is a conjecture in number theory regarding the sequences generated by applying the forward difference opera
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