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Artin primitive-root infinitude for every admissible base

Artin’s conjecture predicts infinitely many primitive-root primes for every admissible fixed base, with a stronger positive-density asymptotic.

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Understanding the problem

Read the background

Artin’s conjecture predicts infinitely many primitive-root primes for every admissible fixed base, with a stronger positive-density asymptotic. The reported lower bound targets the infinitude part.

Constants and the large-x threshold depend on the base. The bound has an extra logarithm compared with the predicted asymptotic and does not establish that density formula.

Why it matters

If correct, proves the infinitude assertion for each admissible base while retaining the distinction from Artin’s density prediction.

What counts as progress

A sourced resolution or substantial advance on the precise target, with hypotheses, prior context, and verification evidence stated separately.

What to watch for

  • Assess the precise statement and assumptions before comparing results.
  • Constants and the large-x threshold depend on the base. The bound has an extra logarithm compared with the predicted asymptotic and does not establish that density formula.
  • Track independent assessments, dependencies, corrections, and withdrawals separately from importance.

Background review: 2026-10-11. Selected sources:

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