# [Simultaneous primitive roots: a conditional lower bound for prime bases](simultaneous-primitive-roots-conditional-lower-bound-prime-bases.pdf)

**Author:** OpenAI

**Date:** October 4, 2026

## Citation

```bibtex
@misc{OAI:Simultaneous-primitive-roots-a-conditional-lower-bound-for-prime-bases-October-4-2026,
  author = {{OpenAI}},
  title = {{Simultaneous primitive roots: a conditional lower bound for prime bases}},
  howpublished = {OpenAI Math Release preprint
                  \href{https://github.com/openai/math/blob/main/preprints/Simultaneous-primitive-roots-a-conditional-lower-bound-for-prime-bases-October-4-2026/simultaneous-primitive-roots-conditional-lower-bound-prime-bases.pdf}{OAI:Simultaneous-primitive-roots-a-conditional-lower-bound-for-prime-bases-October-4-2026}},
  year = {2026}
}
```