The board / number theory / #950
Erdős Problem #950
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 \(f(n) = \sum_{p<n}\frac{1}{n-p}\).
Is it true that \(\liminf f(n)=1\)?
Statement as formalized in Formal Conjectures (Google DeepMind, Apache-2.0) · their label: research open · 6 further variants / known partial results in the Lean file. The authoritative wording is on erdosproblems.com/950.Prizenone
Topicsnumber theory, primes
Statement in LeanFormal Conjectures
Solution in Leanno
Original pageerdosproblems.com/950
Attempts
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modulo Guth–Maynard, \(13/30\le\liminf f\le1\) and \(\limsup f\ge13/30+\log2\); all three questions reduce exactly to \(f(p)\), and exact integer computation certifies the unique extrema through \(2{,
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