2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/222776We suggest a new approach to Artin's constant that leads to its representation as an infinite sum divided by another infinite sum. The same approach works well for Stephens' constant and higher rank Artin's constants. The main results are theoretical but there are interesting experimental and computational aspects.v2: two refferences were added; one graph was improved; v3: Stephens' constant and higher rank Artin's constants are incorporated, the numerical section is extended, editing; v4: the convergence estimates were added and one referenceNumber Theorytext