The function pprimroot(g, n) computes the next primitive root larger than g or, if n does not have primitive roots, computes a number which is not a root of order of any of the factors of .

Thus (in all cases), find an integer y, such that there is no  for which  when r is a divisor of  greater than 1 and .

If only one argument n is present then this function will return the smallest primitive root of the number n. If there is no primitive root of n then this function will return the smallest integer y, such that there is no  for which  when r is a divisor of  greater than 1 and .

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