diff --git a/internal/lib/lib.go b/internal/lib/lib.go
index 2297625..fa0eab7 100644
--- a/internal/lib/lib.go
+++ b/internal/lib/lib.go
@@ -161,12 +161,11 @@ func PrimitiveRootFast(modulus *big.Int, tpf map[string]*big.Int) (*big.Int, err
 
 		isPrimitive := true
 		for p := range tpf {
-			e := new(big.Int)
-			f, _ := new(big.Int).SetString(p, 10)
-			k := new(big.Int).Div(phi, f)
-			e.Exp(g, k, modulus)
-
-			if e.Cmp(big.NewInt(1)) == 0 {
+			// we already know factors are valid from computing phi
+			k, _ := new(big.Int).SetString(p, 10)
+			k.Div(phi, k)
+			k.Exp(g, k, modulus)
+			if k.Cmp(big.NewInt(1)) == 0 {
 				isPrimitive = false
 				break
 			}