Artemis: Optimize Prime-Related Functions for Better Performance

app/src/main/java/algorithms/Primes.java

@@ -12,7 +12,13 @@ public static boolean IsPrime(int n) {
     if (n < 2) {
       return false;
     }
-    for (int i = 2; i * i <= n; i++) { // Optimized loop condition
+    if (n == 2) {
+      return true;
+    }
+    if (n % 2 == 0) {
+      return false;
+    }
+    for (int i = 3; i * i <= n; i += 2) { // Only check odd numbers
       if (n % i == 0) {
         return false;
       }
@@ -28,9 +34,13 @@ public static boolean IsPrime(int n) {
    */
   public static int SumPrimes(int n) {
     int sum = 0;
-    for (int i = 0; i < n; i++) {
+    if (n < 2) {
+      return 0;
+    }
+    sum += 2; // Include 2 as the first prime
+    for (int i = 3; i < n; i += 2) { // Only check odd numbers
       if (IsPrime(i)) {
-        sum = sum + i;
+        sum += i;
       }
     }
     return sum;
@@ -44,16 +54,27 @@ public static int SumPrimes(int n) {
    */
   public static Vector<Integer> PrimeFactors(int n) {
     Vector<Integer> ret = new Vector<Integer>();
+
+    // Handle 2 separately
+    while (n % 2 == 0) {
+      ret.add(2);
+      n /= 2;
+    }
 
-    for (int i = 2; i * i <= n; i++) { // Optimized loop condition
-      while (n % i == 0 && IsPrime(i)) { // Optimized to handle repeated factors
-        ret.add(i);
-        n /= i; // Reduce n to avoid redundant checks.
+    // Check odd numbers only
+    for (int i = 3; i * i <= n; i += 2) {
+      while (n % i == 0) {
+        if (IsPrime(i)) {
+          ret.add(i);
+          n /= i;
+        } else {
+          break;
+        }
       }
     }
     if (n > 1) { // Add any remaining prime factor.
         ret.add(n);
     }
     return ret;
   }
-}
+}