Primitive root modulo n

In modular arithmetic, a number g is a primitive root modulo n, if every number m from 1..(n-1) can be expressed in the form of $g^{x}\equiv m{\pmod {n}}$. As an example, 3 is a primitive root modulo 7:

$3^{1}\equiv 3\ {\pmod {7}}$

$3^{2}\equiv 2\ {\pmod {7}}$

$3^{3}\equiv 6\ {\pmod {7}}$

$3^{4}\equiv 4\ {\pmod {7}}$

$3^{5}\equiv 5\ {\pmod {7}}$

$3^{6}\equiv 1\ {\pmod {7}}$

All the elements $1,2,\ldots ,6$ of the group modulo 7 can be expressed that way. The number 2 is no primitive root modulo 7, because

$2^{3}=8\equiv 1{\pmod {7}}$

and

$2^{6}=64\equiv 1{\pmod {7}}$