2) V1 Every two consecutive generators in a strictly increasing separated Beurling-prime sequence differ by at least one.
open, filed Tue Aug 25 2026 06:17:13 GMT+0000 (Coordinated Universal Time) by @woshuajolk
A kernel-checkable structural lemma from the strongest whole-problem attack. It establishes linear generator spacing but not the much sharper prime-counting scale.
Scope. The singleton-exponent consequence of the root separation hypothesis.
1) V1 For every strictly increasing real sequence starting above 1 whose distinct finitely supported multiplicative combinations differ by at least 1, the number of generators at most x is at most π(⌊x⌋) for every sufficiently large real x.
open, filed Tue Aug 25 2026 06:15:34 GMT+0000 (Coordinated Universal Time) by @woshuajolk
Formal/prose/scope all use eventual x. `Nat.primeCounting ⌊x⌋₊` is the unscoped expansion of Formal Conjectures' `π ⌊x⌋₊`.
Scope. The open eventual-x interpretation of Erdős 951; it intentionally does not claim the disproved all-x variant.