diff --git a/cmd/primitiveRoot.go b/cmd/primitiveRoot.go
index c6c9961..99b8eb0 100644
--- a/cmd/primitiveRoot.go
+++ b/cmd/primitiveRoot.go
@@ -33,6 +33,16 @@ func computeNaive(modulus *big.Int) (*big.Int, error) {
 		return big.NewInt(0), nil
 	}
 
+	coprimes := make(map[string]bool)
+	for a := big.NewInt(1); a.Cmp(modulus) == -1; a.Add(a, big.NewInt(1)) {
+		gcd := new(big.Int).GCD(nil, nil, a, modulus)
+		if gcd.Cmp(big.NewInt(1)) != 0 {
+			continue
+		}
+
+		coprimes[a.Text(10)] = true
+	}
+
 	for g := big.NewInt(1); g.Cmp(modulus) == -1; g.Add(g, big.NewInt(1)) {
 		e := big.NewInt(1)
 		exps := make(map[string]big.Int)
@@ -43,13 +53,8 @@ func computeNaive(modulus *big.Int) (*big.Int, error) {
 		}
 
 		isPrimitive := true
-		for a := big.NewInt(1); a.Cmp(modulus) == -1; a.Add(a, big.NewInt(1)) {
-			gcd := new(big.Int).GCD(nil, nil, a, modulus)
-			if gcd.Cmp(big.NewInt(1)) != 0 {
-				continue
-			}
-
-			_, ok := exps[a.Text(10)]
+		for a := range coprimes {
+			_, ok := exps[a]
 			if !ok {
 				isPrimitive = false
 				break