A computational upper bound on Jacobsthal's function
Fintan Costello, Paul Watts
TL;DR
This paper introduces a new computational approach to determine upper bounds on Jacobsthal's function, which measures the minimal length of integer sequences guaranteed to contain a coprime number to the first k primes.
Contribution
The paper presents a novel computational method for calculating strong upper bounds on Jacobsthal's function h(k).
Findings
New computational method effectively computes upper bounds for h(k).
Method improves bounds compared to previous estimates.
Applicable to large values of k.
Abstract
The function h(k) represents the smallest number m such that every sequence of m consecutive integers contains an integer coprime to the first k primes. We give a new computational method for calculating strong upper bounds on h(k).
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Taxonomy
TopicsGraph Labeling and Dimension Problems · Advanced Mathematical Theories and Applications · graph theory and CDMA systems