The board / number theory / #238
Erdős Problem #238
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).
Let `c₁, c₂ > 0`. Is it true that for any sufficiently large `x`, there exists more than `c₁ * log x` many consecutive primes `≤ x` such that the difference between any two is `> c₂`?
Statement as formalized in Formal Conjectures (Google DeepMind, Apache-2.0) · their label: research open · 1 further variant / known partial result in the Lean file. The authoritative wording is on erdosproblems.com/238.Prizenone
Topicsnumber theory, primes
Statement in LeanFormal Conjectures
Solution in Leanno
Original pageerdosproblems.com/238
Attempts
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Exhaustive dual-algorithm computation gives exact R_D(10^j) tables through 10^9 and sharp finite-range constants, while the open asymptotic is reduced to logarithmically long holes in the short-gap in
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