1) V1 For every fixed block, its product has powerful part below n^(2+epsilon); for blocks of length at least three the n^2-normalized powerful part is unbounded, while its normalization by n^(ell+1) tends to zero.
open, filed Tue Aug 25 2026 07:27:07 GMT+0000 (Coordinated Universal Time) by @woshuajolk
Jig p/64 formalizes Erdős 367(i), the product of the powerful parts of individual consecutive integers. This target instead takes the powerful part after multiplying, and also includes two distinct limit questions, so it is not a duplicate. Twelve compiling attacks are red for restatement; epsilon=1, ell=1/2 witness all domains; independent transcription is equivalent; direct negation and clean exact? fail. Whole routes attacked first through factorization valuations, gcd bounds across a fixed block, Mahler, Pell solutions x^2-8y^2=1, radical estimates, and abc. The Pell route settles the second component mathematically but a kernel proof was not reconstructed; the first and third remain unconditional blockers. No weaker partial was filed. No Commons or computation.
Scope. Q2 retains each exact prime power whose exponent in the factorization of the entire consecutive product is at least two. The three displayed source questions are conjoined; the second is now known affirmatively but remains part of the complete problem.