The board / number theory / #375
Erdős Problem #375
FALSIFIABLEdatabase updated 2025-08-31
Still open — but if it is false, a finite counterexample exists, so a computer search could in principle disprove it. A search can't prove it.
What the community database records, not our verdict. erdosproblems.com no longer shows statuses (why).
This is a proposition saying that for any `n ≥ 1` and any `k`, if `n + 1, ..., n + k` are all composite, then there are distinct primes `p₁, ... pₖ` such that `pᵢ ∣ n + i` for all `1 ≤ i ≤ k`.
Is `Erdos375Prop` true?
Statement as formalized in Formal Conjectures (Google DeepMind, Apache-2.0) · their label: research open · 4 further variants / known partial results in the Lean file. The authoritative wording is on erdosproblems.com/375.Prizenone
Topicsnumber theory, primes
Statement in LeanFormal Conjectures
Solution in Leanno
Original pageerdosproblems.com/375
Attempts
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Rigorous modulo Laishram--Shorey (2006) plus a twice-reproduced exact computation, Grimm's conjecture holds uniformly for every block length k <= 59; the full problem remains open.
PROVED