Least primitive root

From Number
Jump to: navigation, search


Suppose is a natural number such that the multiplicative group modulo is cyclic (i.e., is either a prime number, or , or a power of an odd prime, or twice the power of an odd prime). The least primitive root or smallest primitive root modulo is the smallest natural number such that is a primitive root modulo .

Particular cases

Here, we only list equal to a prime or the square of a prime. For something that is a higher power of an odd prime, the smallest primitive root modulo the square of the prime works.

Smallest primitive root modulo
2 1
3 2
4 3
5 2
7 3
11 2
13 2
17 3