I'm not an expert, but the content of the article Artin's primitive root conjecture -a survey - (modified December 2004) by Pieter Moree suggests the Wikipedia article is reasonably up-to-date.
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added article's title and author for searchability, updated arXiv link to point to v1 of the article since that is what this answer references
The Amplitwist
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S. Carnahan ♦
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