Erdős Problem #200
OPENdatabase updated 2025-08-31
No proof or disproof is known, and it isn't known whether a finite computation could settle it.
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The length of the longest arithmetic progression of primes in \(\{1,\ldots,n\}\).
Does the longest arithmetic progression of primes in \(\{1,\ldots,N\}\) have length \(o(\log N)\)?
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/200.Prizenone
Topicsprimes, arithmetic progressions
Statement in LeanFormal Conjectures
Solution in Leanno
OEISA005115
Original pageerdosproblems.com/200
Attempts
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