Algorithmic concepts for the computation of Jacobsthal's function

Abstract

The Jacobsthal function has aroused interest in various contexts in the past decades. We review several algorithmic ideas for the computation of Jacobsthal's function for primorial numbers and discuss their practicability regarding computational effort. The respective function values were computed for primes up to 251. In addition to the results including previously unknown data, we provide exhaustive lists of all sequences of the appropriate maximum lengths in ancillary files.

27 pages, 2 figures, 1 table, v2: revised description, results unchanged

Cited by in corpus (5)

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• Divisibility in paired progressions, Goldbach's conjecture, and the infinitude of prime pairs
• New computational results on a conjecture of Jacobsthal
• On differences between consecutive numbers coprime to primorials
• A short note on the computation of the generalised Jacobsthal function for paired progressions