From 85eb1d4ea88c8adf4ec7029f8fc444e89e730066 Mon Sep 17 00:00:00 2001
From: swayam patil <swayampatil7803@gmail.com>
Date: Fri, 21 Apr 2023 22:25:30 +0530
Subject: [PATCH] Create Miller-Rabin_primalityTest.cpp

This code checks if a given number is likely to be a prime using the Miller-Rabin primality test, which is a probabilistic algorithm. The algorithm chooses a random number and tests whether it is a witness for the compositeness of the given number. This is repeated a number of times to increase the confidence in the result. If the number passes all tests, it is considered likely to be prime.
---
 Miller-Rabin_primalityTest.cpp | 48 ++++++++++++++++++++++++++++++++++
 1 file changed, 48 insertions(+)
 create mode 100644 Miller-Rabin_primalityTest.cpp

diff --git a/Miller-Rabin_primalityTest.cpp b/Miller-Rabin_primalityTest.cpp
new file mode 100644
index 0000000..467a7e9
--- /dev/null
+++ b/Miller-Rabin_primalityTest.cpp
@@ -0,0 +1,48 @@
+#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;
+}