Grimm's conjecture states that for every set of consecutive composite numbers, there is an equally sized set of prime numbers with a bijection mapping each composite to a prime that divides it. It was first proposed by Carl Albert Grimm in 1969 and, though still unproven, has been verified for all n below 1.9 times ten to the tenth. 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
StatementIf n+1, n+2, ..., n+k are all composite numbers, then there is a sequence of distinct prime numbers p_1, ..., p_k such that p_i divides n+i for 1 <= i <= k. 1 Proposed Year Progress Toward ResolutionStill unproven, but verified for all n below 1.9 times ten to the tenth. 1 Classification
Resolution Status Prize Status
Prize Status (category) Connections
In Branch
Source Grimm's Conjecture (Wikipedia)
Sources
1. Grimm's Conjecture (Wikipedia)
Wikimedia FoundationLead section
first proposed by Carl Albert Grimm in 1969
Formal statement
then there is a sequence of distinct prime numbers
Lead section, second paragraph
Though still unproven, the conjecture has been verified for all
In Branch: Number Theory, Lead sentence
In mathematics, specifically in number theory, Grimm's conjecture states that, for every set of consecutive composite numbers, the
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