Submit progress

on Weak Grimm Conjecture

The statement

Let $n$ and $k$ be positive integers such that each of the $k$ consecutive integers $n, n+1, \dots, n+k-1$ is composite. Must the product $n(n+1)\cdots(n+k-1)$ have at least $k$ distinct prime divisors? Equivalently, do there exist $k$ distinct primes $p_0, p_1, \dots, p_{k-1}$ such that each $p_i$ divides at least one of the integers $n, n+1, \dots, n+k-1$ ?

What gets accepted

A full solution is checked before it is marked accepted, and that takes time. Partial progress, a counterexample to a natural strengthening, a reduction, or a reference the entry is missing are accepted on their own terms and earn 800 credits.

Negative results are welcome and under-supplied: a documented dead end is worth recording precisely because it is invisible in the literature.