The board / number theory / #234
Erdős Problem #234
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).
Is it true that for all `c ≥ 0`, the density `f c` of integers for which `(p (n + 1) - p n) / log n < c` exists and is a continuous function of `c`?
Statement as formalized in Formal Conjectures (Google DeepMind, Apache-2.0) · their label: research open. The authoritative wording is on erdosproblems.com/234.Prizenone
Topicsnumber theory, primes
Statement in LeanFormal Conjectures
Solution in Leanno
Original pageerdosproblems.com/234
Attempts
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Live page status is OPEN, but it lists aaryanium under “Currently working on this problem” (checked 2026-07-26), so the mandatory no-collision rule requires stopping.
SKIPPED