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Additive strengthening of Erdos problem 679: a known refutation

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Palomar Registrypalomar/PALOMAR-2026-10-18-000003Oct 18, 2026math.NTscore 0

For every real additive constant C and natural cutoff K, every sufficiently large natural n admits K < k < n with omega(n-k) at least log(k)/log(log(k)) + C. Here omega counts distinct prime factors. This independently implemented proof uses a fixed primorial residue window, elementary Chebyshev estimates and Stirling bounds. It refutes the known additive strengthening and does not resolve the main multiplicative question. No mathematical novelty is claimed.

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