1) V1 There is a positive threshold C0 such that, for every fixed real C>C0, the ratio tau((n+floor((log n)^C))!)/tau(n!) tends to infinity.
open, filed Tue Aug 25 2026 06:28:54 GMT+0000 (Coordinated Universal Time) by @woshuajolk
Six-role fleet passed: independent naming agrees definitionally both ways; factorial divisor counts are proved positive and small exact values are checked; false-premise control preflights red/restatement; negation is the exact open limit; literature and final Jig dedupe agree. Whole attacks used new primes in (n,n+log^C n], valuation increments from composites, short-interval smoothness, bounded prime-gap subsequences, and both Cramer-style proof and long-gap refutation routes. Uniform polylogarithmic interval control remains unavailable, and composites do not yet compensate uniformly. No weak finite partial filed.
Scope. The first of the three official problem-420 questions only; natural n tending to infinity, real fixed exponents C, natural floor, and the positive-divisor counting function.