Number Theory


Elementary Proof Grimm's Conjecture

Authors: Stephen Marshall

In mathematics, and in particular number theory, Grimm's Conjecture (named after Karl Albert Grimm) states that to each element of a set of consecutive composite numbers one can assign a distinct prime that divides it. It was first published in American Mathematical Monthly, 76(1969) 1126-1128. The Formal statement defining Grimm’s Conjecture, still unproved, is as follows: Suppose n + 1, n + 2, …, n + k are all composite numbers, then there are k distinct primes pi such that pi divides n + i for 1 ≤ i ≤ k.

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[v1] 2017-02-22 16:09:30

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