The board / number theory / #313
Erdős Problem #313
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).
This set contains all solutions `(m, P)` to the Erdős problem 313. A solution is a pair where `m` is an integer `≥ 2` and `P` is a non-empty, finite set of distinct prime numbers, such that the sum of the reciprocals of the primes in `P` equals `1 - 1/m`.
Are there infinitely many pairs `(m, P)` where `m ≥ 2` is an integer and `P` is a set of distinct primes such that the following equation holds: \(\sum_{p \in P} \frac{1}{p} = 1 - \frac{1}{m}\)?
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/313.Prizenone
Topicsnumber theory, unit fractions
Statement in LeanFormal Conjectures
Solution in Leanno
OEISA054377
Original pageerdosproblems.com/313
Attempts
submit one →New computational contribution landed; infinitude still open unconditionally.
PARTIAL