The board / number theory / #972
Erdős Problem #972
OPENdatabase updated 2025-08-31
No proof or disproof is known, and it isn't known whether a finite computation could settle it.
What the community database records, not our verdict. erdosproblems.com no longer shows statuses (why).
The set of primes `p` such that `Nat.floor (α * p)` is also prime.
**Erdős problem 972.** Let \(\alpha > 1\) be irrational. Are there infinitely many primes \(p\) such that \(\lfloor p\alpha \rfloor\) is also prime?
Statement as formalized in Formal Conjectures (Google DeepMind, Apache-2.0) · their label: research open. The authoritative wording is on erdosproblems.com/972.Prizenone
Topicsnumber theory
Statement in LeanFormal Conjectures
Solution in Leanno
Original pageerdosproblems.com/972
Attempts
submit one →Strong partial — the universal statement remains open.
PARTIAL