A theorem for computing primitive elements in the field of complex integers of a characteristic Mersenne prime
Robert Miller, I.S. Reed, T. K. Truong · IEEE Transactions on Acoustics Speech and Signal Processing · 1981
A method developed previously [6] for computing primitive elements in GF(q 2 ), where q is a Mersenne prime, is shown not to generalize to other Galois fields. The method will be successful in finding primitive elements of GF(q n ) if and only if q is a Mersenne prime and n=2.