Create Miller-Rabin_primalityTest.cpp

Miller-Rabin_primalityTest.cpp

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+#include <iostream>
+#include <cstdlib>
+#include <cmath>
+
+using namespace std;
+
+bool miller_rabin(long long n, int k=5) {
+  // Check some basic primality conditions
+  if (n < 2) {
+    return false;
+  }
+  if (n == 2 || n == 3) {
+    return true;
+  }
+  if (n % 2 == 0) {
+    return false;
+  }
+
+  // Write n-1 as d * 2^r, where d is odd
+  long long d = n - 1;
+  int r = 0;
+  while (d % 2 == 0) {
+    d /= 2;
+    r++;
+  }
+
+  // Perform the Miller-Rabin test k times
+  for (int i = 0; i < k; i++) {
+    // Choose a random witness a in the range [2, n-2]
+    long long a = rand() % (n - 3) + 2;
+    long long x = pow(a, d) % n;
+
+    // Check whether a is a witness for the compositeness of n
+    if (x == 1 || x == n - 1) {
+      continue;
+    }
+    for (int j = 0; j < r - 1; j++) {
+      x = (x * x) % n;
+      if (x == n - 1) {
+        break;
+      }
+    }
+    if (x != n - 1) {
+      return false;
+    }
+  }
+  return true;
+}