Problem 383

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 $p$ ?

Source: erdosproblems.com/383

Number theory

Wiki page

Status

Open

No claim settles this problem.

Open, the site's label (OPEN; the site marks the problem as not decidable by a finite computation). Its proof-claims tab carries one partial proof claim, submitted 2026-07-25 and without response which settles no case of the question and gets no claim page; the Current assessment records it with the reason.

Problem 383

Status

Proof claims

Discussion