Grimm's conjecture
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In mathematics, and in particular number theory, Grimm's conjecture 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.
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[edit] Formal statement
Suppose n + 1,n + 2,...,n + k are all composite numbers, then there are distinct primes pi such that pi | (n + i) for 
.
[edit] Weaker version
A weaker, though still unproven, version of this conjecture goes: If there is no prime in the interval [n + 1,n + k], then 
has at least k distinct prime divisors.
[edit] See also
[edit] References
- Eric W. Weisstein, Grimm's Conjecture at MathWorld.
- Guy, R. K. "Grimm's Conjecture." §B32 in Unsolved Problems in Number Theory, 2nd ed. New York: Springer-Verlag, p. 86, 1994.
