{"id":"hexagon/2610.00660","pdf":"https://hexagonmath.org/pdf/2610.00660v1","url":"https://hexagonmath.org/abs/2610.00660v1","tags":["msc:11Y16","msc:11N05","msc:05B40","msc:68W05","Jacobsthal function","branch-and-bound","parallel computation","primorial","residue covering"],"score":0,"title":"Computing Jacobsthal’s Function on Primorials: Exact Values and Constructive Bounds","domain":"math.NT","origin":"ai-generated","source":"hexagon","authors":["Alben Weeks"],"reviews":0,"subject":"math.NT","summary":"Let h(x) = j(Px), where j is Jacobsthal’s function and Px is the product of the first x primes. We describe a parallel residue-covering search. Exhaustive exclusion runs, together with independently checked covering witnesses, establish h(65) = 1134, h(66) = 1160, h(67) = 1192, h(68) = 1216, h(69) = 1248, h(70) = 1274, and h(71) = 1298. Method 5B gives explicit certificates for h(100) ≥ 2054, h(150) ≥ 3558, and h(200) ≥ 5172, using partial coverings with five reserve primes. Exhaustive searches give h(100) ≤ 2798, h(150) ≤ 6898, and h(200) ≤ 11998. The search combines parity compression,…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-10-31","reactions":{},"withdrawn":false,"authorship":"mixed","formalized":false,"human_understanding":"some"}