diff --git a/mathx/number_theory.h b/mathx/number_theory.h
index 0572f3e..24cffaa 100644
--- a/mathx/number_theory.h
+++ b/mathx/number_theory.h
@@ -2,8 +2,11 @@
 #define MATHX_NUMBER_THEORY_H_
 
 namespace mathx {
-    int gcd(int a, int b);
-    int lcm(int a, int b);
+    long long gcd(long long a, long long b);
+    long long lcm(long long a, long long b);
+    long long pow(long long a, long long e, long long mod);
+    bool is_miller_rabin_witness(long long a, long long p);
+    bool is_prime_fast(long long p);
 }
 
 #endif
diff --git a/src/number_theory.cpp b/src/number_theory.cpp
index a3c66a5..5a52654 100644
--- a/src/number_theory.cpp
+++ b/src/number_theory.cpp
@@ -1,7 +1,7 @@
 #include <number_theory.h>
 
 namespace mathx {
-    int gcd(int a, int b) {
+    long long gcd(long long a, long long b) {
         while( a * b ){
             if(a > b)
                 a = a % b;
@@ -10,7 +10,63 @@ namespace mathx {
         }
         return a + b;
     }
-    int lcm(int a, int b) {
+
+    long long lcm(long long a, long long b) {
         return (a * b / gcd(a,b));
     }
+
+    long long pow(long long a, long long e, long long mod) {
+        if (e == 0) {
+            return 1;
+        }
+
+        long long x = mathx::pow(a, e / 2, mod);
+        if (e % 2 == 0) {
+            return (x * x) % mod;
+        }
+        else {
+            return (((x * x) % mod) * x) % mod;
+        }
+    }
+
+    bool is_miller_rabin_witness(long long a, long long p) {
+        long long g = mathx::gcd(a,p);
+        if (g == 1) {
+            return true;
+        }
+
+        long long k = 0;
+        long long q = p - 1;
+        while (q % 2 == 0) {
+            q = q / 2;
+            ++k;
+        }
+        long long temp = mathx::pow(a, q, p);
+        if (temp == 1) {
+            return false;
+        }
+
+        for (int i = 0; i < k; ++i) {
+            if (temp == p - 1) {
+                return false;
+            }
+            else {
+                temp = (temp * temp) % p;
+            }
+        }
+        return true;
+    }
+
+
+    bool is_prime_fast(long long p) {
+        if (p == 1) {
+            return false;
+        }
+        for (int i = 0; i < 100; ++i) {
+            if (mathx::is_miller_rabin_witness(i, p) == true) {
+                return false;
+            }
+        }
+        return true;
+    }
 }