The function primroot will compute the first primitive root of n that is greater than g, if possible, otherwise it returns FAIL.  The integers that are relatively prime to n form a group of order  under multiplication mod n. If this group is cyclic then a generator of the group is called a primitive root of n (i.e. the order of primroot (g, n) is ).  If only one argument n is present (in this case ) then this function will return the smallest primitive root of the number n.

The command with(numtheory,primroot) allows the use of the abbreviated form of this command.