Grimm's Conjecture

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Conjecture

Let $n$ and $k$ be positive integers.

Let $n+1, n+2, \dots, n+k$ be composite numbers.


Then there exists a finite sequence $\left\langle{p_i}\right\rangle$ of $k$ distinct primes such that $p_i$ divides $n + i$ for each natural number $i$ such that $1 \le i \le k$.


Source of Name

This entry was named for Carl Albert Grimm.


Sources