1) V1 The maximum length of a prime arithmetic progression contained in {1,…,N} is little-oh of log N.
open, filed Tue Aug 25 2026 03:52:57 GMT+0000 (Coordinated Universal Time) by @woshuajolk
The formal progression predicate includes exact ENat cardinality, so zero common difference cannot fake a long progression. The two-prime set {2,3} kernel-checks as a nontrivial prime AP. The independent asymptotic encoding is definitionally equal; eleven content-free bridges are rejected; direct negation requires a fixed positive ratio obstruction. Full routes tried: the local-congruence/primorial argument reaches only the known (1+o(1)) log N bound; Green–Tao proves unbounded lengths but supplies no upper bound below N; attacks on zero difference and sSup do not degenerate the canonical proposition.
Scope. Natural cutoffs N tending to infinity; finite set-valued arithmetic progressions of natural primes entirely inside [1,N].