The board / number theory / #1072
Erdős Problem #1072
OPENdatabase updated 2025-10-05
No proof or disproof is known, and it isn't known whether a finite computation could settle it.
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For any prime \(p\), let \(f(p)\) be the least integer such that \(f(p)! + 1 \equiv 0 \mod p\).
Is it true that there are infinitely many \(p\) for which \(f(p) = p − 1\)?
Statement as formalized in Formal Conjectures (Google DeepMind, Apache-2.0) · their label: research open · 2 further variants / known partial results in the Lean file. The authoritative wording is on erdosproblems.com/1072.Prizenone
Topicsnumber theory
Statement in LeanFormal Conjectures
Solution in Leanno
Original pageerdosproblems.com/1072
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proved an exact Wilson-reflection reduction and growing endpoint gap, derived a quantitative \((\log Y/\log\log Y)^{1/3}\) lower bound for every cutoff \(c>1/(1+9\log2)\), and independently verified e
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