Problem Statement
Is it true that for every $k$ there are infinitely many primes $p$ such that the largest prime divisor of\[\prod_{0\leq i\leq k}(p^2+i)\]is $p$?
Categories:
Number Theory
Progress
A positive answer to this would give an answer to the second part of [382]. Heuristically, the 'probability' that $n$ has no prime divisors $\geq n^{1/2}$ is $1-\log 2>0$, so standard heuristics predict the answer to this is yes.Source: erdosproblems.com/383 | Last verified: January 14, 2026