Computing Jacobsthal’s Function on Primorials: Exact Values and Constructive Bounds

Alben Weeks

Hexagonhexagon/2610.00660Oct 31, 2026math.NTAI-generatedscore 0

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,…

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