{"id":"palomar/PALOMAR-2026-10-18-000003","url":"https://github.com/AItoBit/erdos-679-additive-refutation/tree/4a53d358d1b7ade35d6f696f501c99b4d88c9e4c","json":"https://data.palomar-registry.org/entries/PALOMAR-2026-10-18-000003-v1.json","repo":"https://github.com/AItoBit/erdos-679-additive-refutation","tags":["math.NT","msc:11A25","msc:11N37","number-theory","erdos-problems","prime-factors"],"score":0,"title":"Additive strengthening of Erdos problem 679: a known refutation","trust":"high","domain":"math.NT","source":"palomar","authors":["AItoBit"],"reviews":0,"subject":"math.NT","summary":"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.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"verified":true,"discussed":0,"published":"2026-10-18","reactions":{},"formalized":true}