For an odd prime $p$ and an exponent $e\geq1$, the group $(\Z/p^e\Z)^\times$ is cyclic. It happens that any integer $a$ which generates $(\Z/p^2\Z)^\times$ will also be a generator of $(\Z/p^e\Z)^\times$ for all $e\geq 1$. We call the least such $a$ the **Conrey (primitive) generator** modulo p.

Interestingly, the Conrey generator is also the smallest generator of $(\Z/p\Z)^\times$ for all primes $p<10^{12}$ except two cases:

- for $p=40487$, the Conrey generator is $10$ instead of $5$.
- for $p=6692367337$, the Conrey generator is $7$ instead of $5$.

**Authors:**

**Knowl status:**

- Review status: reviewed
- Last edited by Kiran S. Kedlaya on 2018-07-04 19:45:22

**Referred to by:**

**History:**(expand/hide all)

- 2018-07-04 19:45:22 by Kiran S. Kedlaya (Reviewed)