# Artin's conjecture on primitive roots for two

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## Statement

This is a special case of Artin's conjecture on primitive roots for the number . It is still open.

### Infinitude version

There are infinitely many primes  such that  is a primitive root modulo .

### Density version

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## Relation with other facts and conjectures

### Related facts

• Heath-Brown theorem on Artin's conjecture states that Artin's conjecture holds for all but at most two exceptional numbers. However, it gives no explicit information about what those two numbers may be, and hence  may be one of those exceptional numbers.