The board / additive combinatorics / #141
Erdős Problem #141
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 predicate that a set `s` consists of `l` consecutive primes (possibly infinite). This predicate does not assert a specific value for the first term.
The predicate that a set `s` is both an arithmetic progression of length `l` and a progression of `l` consecutive primes.
Let \(k≥3\). Are there \(k\) consecutive primes in arithmetic progression?
Statement as formalized in Formal Conjectures (Google DeepMind, Apache-2.0) · their label: research open · 4 further variants / known partial results in the Lean file. The authoritative wording is on erdosproblems.com/141.Prizenone
Statement in LeanFormal Conjectures
Solution in Leanno
OEISA006560
Original pageerdosproblems.com/141
Attempts
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Verified the published CPAP-10 from embedded ECPP certificates, computationally verified that no CPAP-7 ends by 10^9, and reduced the general case conditionally to explicit admissible linear forms; no
PARTIAL