The TME-EMT project

Navigation

Back to top

---

Primitive Roots

---

As a consequence of , we find the next result.
Theorem (2020)

The least primitive root $g(p)$ modulo the prime $p$ satisfies $g(p)\le p^{5/8}$ when $p\ge 10^{22}$ and $g(p) < \sqrt{p}-2$ when $p\ge 10^{56}$.

From , we also have:
Theorem (2016)

Under GRH, the least primitive root $g(p)$ modulo the prime $p$ satisfies $g(p) < \sqrt{p}-2$ for every $p > 409$.

Similar investigations concerning primivite roots modulo $p^2$ are led in and in where the next theorem is proved.
Theorem (2022)

The least primitive root $h(p)$ modulo $p^2$ satisfies $h(p)\le p^{0.74}$ for all $p \ge 2$.

---