The different constructions of perfect Gaussian integer sequences (PGISs) have been extensively investigated in the recent literature. Those sequences have also been applied in a wide range of comb-spectrum code division multiple access as well as precoded orthogonal frequency-division multiplexing systems. This paper presents the long PGISs of primitive length based on the novel polynomial computations over finite fields. Such a polynomial can be expressed by the newly discovered exponent, which is less than the previously known Kasami exponent. This fact leads to the fast generation of long PGISs.