Grimm's Conjecture

Grimm conjectures that if $n+1$, $n+2$, ..., $n+k$ are all Composite Numbers, then there are distinct Primes $p_{i_j}$ such that $p_{i_j}\vert(n+j)$ for $1\leq j\leq k$.

References

Guy, R. K. ``Grimm's Conjecture.'' §B32 in Unsolved Problems in Number Theory, 2nd ed. New York: Springer-Verlag, p. 86, 1994.