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Conjecture

Grimm's Conjecture

Number Theory

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
Statement
If 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
1969 1
Progress Toward Resolution
Still unproven, but verified for all n below 1.9 times ten to the tenth. 1
Classification
Resolution Status
Open 1
Prize Status
Prize Status (category)
No Prize Offered 1
Connections

In Branch

Source Grimm's Conjecture (Wikipedia)
Sources
1. Grimm's Conjecture (Wikipedia)
Wikimedia Foundation
  • Lead 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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