diff --git a/src/maths.c b/src/maths.c
index 9f48ebe..dfed2a1 100755
--- a/src/maths.c
+++ b/src/maths.c
@@ -5,6 +5,7 @@
 
 extern int128_t LIMIT;
 extern int run_bfs(int128_t* sum, int128_t a0, int128_t b0, int128_t c0, int print_mode);
+extern int is_new_root(int128_t a, int128_t b, int128_t c);
 
 const int NUM_PRIMES = 3;
 const int primes[] = {2, 3, 5};
@@ -57,15 +58,21 @@ void generate_factor_pairs(int128_t* sum, int prime_index, int* exponents,
 		if ((n1 + n2) % 2 == 0) {
 			int128_t val1 = values[1] + values[2] + ((n1 + n2) >> 1);
 			int128_t val2 = values[1] + values[2] - ((n1 + n2) >> 1);	
-			int128_t greater = values[2] >= val1 ? values[2] : val1;
+
 			int128_t gcd1 = gcd3(values[1], values[2], val1);
 			int128_t gcd2 = gcd3(values[1], values[2], val2);
-			LIMIT = values[1] >= greater ? values[1] * greater / (2 * gcd1 * gcd1) : values[2] * val1 / (2 * gcd1 * gcd1);
-			run_bfs(sum, values[1] / gcd1, values[2] / gcd1, val1 / gcd1, print_mode);
-			if (val2 >= 0) {
-				greater = values[2] >= val2 ? values[2] : val2;
-				LIMIT =values[1] >= greater ? values[1] * greater / (2 * gcd2 * gcd2) : values[2] * val2 / (2 * gcd2 * gcd2);
-				run_bfs(sum, values[1] / gcd2, values[2] / gcd2, val2 / gcd2, print_mode);
+			int128_t r1a = values[1] / gcd1, r1b = values[2] / gcd1, r1c = val1 / gcd1;
+			int128_t r2a = values[1] / gcd2, r2b = values[2] / gcd2, r2c = val2 / gcd2;
+
+			if (is_new_root(r1a, r1b, r1c)) {
+        		int128_t greater = values[2] >= val1 ? values[2] : val1;
+        		LIMIT = values[1] >= greater ? values[1] * greater / (2 * gcd1 * gcd1) : values[2] * val1 / (2 * gcd1 * gcd1);
+		        run_bfs(sum, r1a, r1b, r1c, print_mode);
+			}
+			if (val2 >= 0 && is_new_root(r2a, r2b, r2c)) {
+				int128_t greater = values[2] >= val2 ? values[2] : val2;
+				LIMIT = values[1] >= greater ? values[1] * greater / (2 * gcd2 * gcd2) : values[2] * val2 / (2 * gcd2 * gcd2);
+		        run_bfs(sum, r2a, r2b, r2c, print_mode);
 			}
 		}
 	return;
diff --git a/src/stergios.c b/src/stergios.c
index 7136e4e..e4b90b3 100755
--- a/src/stergios.c
+++ b/src/stergios.c
@@ -7,6 +7,65 @@
 #define HASH_SIZE 200003
 int128_t LIMIT = 0;
 
+typedef struct GlobalEntry {
+    int128_t a, b, c;
+    struct GlobalEntry* next;
+} GlobalEntry;
+
+static GlobalEntry* global_root_table[HASH_SIZE] = {0};
+
+// Helper to sort the triplet so order doesn't matter
+static void sort_triplet(int128_t* a, int128_t* b, int128_t* c) {
+    int128_t tmp;
+    if (*a > *b) { tmp = *a; *a = *b; *b = tmp; }
+    if (*b > *c) { tmp = *b; *b = *c; *c = tmp; }
+    if (*a > *b) { tmp = *a; *a = *b; *b = tmp; }
+}
+
+static inline uint128_t mix128(uint128_t a, uint128_t b, uint128_t c) {
+    uint128_t x = a + (uint128_t)0x9e3779b97f4a7c15ULL + ((uint128_t)0x9e3779b97f4a7c15ULL << 64);
+    x ^= b + ((uint128_t)0xbf58476d1ce4e5b9ULL + ((uint128_t)0xbf58476d1ce4e5b9ULL << 64)) + (x << 6) + (x >> 2);
+    x ^= c + ((uint128_t)0x94d049bb133111ebULL + ((uint128_t)0x94d049bb133111ebULL << 64)) + (x << 6) + (x >> 2);
+    return x;
+}
+
+static unsigned int hash_three128(uint128_t a, uint128_t b, uint128_t c) {
+	uint128_t x = mix128(a, b, c);
+	return (unsigned int)(x % HASH_SIZE);
+}
+
+// Returns 1 if this is a new root, 0 if we've already calculated it
+int is_new_root(int128_t a, int128_t b, int128_t c) {
+    sort_triplet(&a, &b, &c);
+    unsigned int h = hash_three128((uint128_t)a, (uint128_t)b, (uint128_t)c);
+    
+    GlobalEntry* cur = global_root_table[h];
+    while (cur) {
+        if (cur->a == a && cur->b == b && cur->c == c) return 0;
+        cur = cur->next;
+    }
+    
+    GlobalEntry* e = malloc(sizeof(GlobalEntry));
+    if (!e) return 1; // Fallback to running BFS if malloc fails
+    e->a = a; e->b = b; e->c = c;
+    e->next = global_root_table[h];
+    global_root_table[h] = e;
+    return 1;
+}
+
+// Call this at the start of 'auto' mode
+void clear_global_table() {
+    for (int i = 0; i < HASH_SIZE; i++) {
+        GlobalEntry* cur = global_root_table[i];
+        while (cur) {
+            GlobalEntry* next = cur->next;
+            free(cur);
+            cur = next;
+        }
+        global_root_table[i] = NULL;
+    }
+}
+
 typedef struct Node {
 	int128_t a, b, c;
 	char move;
@@ -36,17 +95,6 @@ void clear_hash_table() {
 
 int run_bfs(int128_t* sum, int128_t a0, int128_t b0, int128_t c0, int print_mode);
 
-static inline uint128_t mix128(uint128_t a, uint128_t b, uint128_t c) {
-    uint128_t x = a + (uint128_t)0x9e3779b97f4a7c15ULL + ((uint128_t)0x9e3779b97f4a7c15ULL << 64);
-    x ^= b + ((uint128_t)0xbf58476d1ce4e5b9ULL + ((uint128_t)0xbf58476d1ce4e5b9ULL << 64)) + (x << 6) + (x >> 2);
-    x ^= c + ((uint128_t)0x94d049bb133111ebULL + ((uint128_t)0x94d049bb133111ebULL << 64)) + (x << 6) + (x >> 2);
-    return x;
-}
-
-static unsigned int hash_three128(uint128_t a, uint128_t b, uint128_t c) {
-	uint128_t x = mix128(a, b, c);
-	return (unsigned int)(x % HASH_SIZE);
-}
 
 static int visit_and_mark(int128_t a, int128_t b, int128_t c) {
 	unsigned int h = hash_three128(a,b,c);
@@ -202,6 +250,7 @@ int main() {
 
 		run_bfs(&sum, a0 / gcd, b0 / gcd, c0 / gcd, print_mode);
 	} else if (mode == 2) {
+		clear_global_table(); // Reset unique root tracker
 		int p = 3;
 		int exponents[3] = {2*p + 2, p, p};
 		int128_t values[3] = {4 * power(a0, p) * power(b0, p), power(a0, p), power(b0, p)};