Grimm's conjecture

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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.

Formal statement[edit]

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.

Weaker version[edit]

A weaker, though still unproven, version of this conjecture goes: If there is no prime in the interval , then has at least k distinct prime divisors.

See also[edit]