The authors recently proved that for a semiprime ring without
2
2
-torsion, a nilpotent derivation must have odd nilpotency. In this paper, we show the intriguing phenomenon that for a semiprime ring with characteristic 2, the nilpotency of a nilpotent derivation must be of the form
2
n
{2^n}
. Combining these two results, we show that for a general semiprime ring with no torsion condition, the nilpotency of a nilpotent derivation is either odd or a power of 2.