Java implementation of Miller-Rabin Primality Test

Author: kyscg

Diff for: Math/miller_rabin_primality_test/mrp.java

@@ -0,0 +1,107 @@
+// Java program Miller-Rabin primality test 
+import java.io.*; 
+import java.math.*; 
+
+class GFG { 
+
+	// Utility function to do modular 
+	// exponentiation. It returns (x^y) % p 
+	static int power(int x, int y, int p) { 
+		
+		int res = 1; // Initialize result 
+		
+		//Update x if it is more than or 
+		// equal to p 
+		x = x % p; 
+
+		while (y > 0) { 
+			
+			// If y is odd, multiply x with result 
+			if ((y & 1) == 1) 
+				res = (res * x) % p; 
+		
+			// y must be even now 
+			y = y >> 1; // y = y/2 
+			x = (x * x) % p; 
+		} 
+		
+		return res; 
+	} 
+	
+	// This function is called for all k trials. 
+	// It returns false if n is composite and 
+	// returns false if n is probably prime. 
+	// d is an odd number such that d*2<sup>r</sup> 
+	// = n-1 for some r >= 1 
+	static boolean miillerTest(int d, int n) { 
+		
+		// Pick a random number in [2..n-2] 
+		// Corner cases make sure that n > 4 
+		int a = 2 + (int)(Math.random() % (n - 4)); 
+	
+		// Compute a^d % n 
+		int x = power(a, d, n); 
+	
+		if (x == 1 || x == n - 1) 
+			return true; 
+	
+		// Keep squaring x while one of the 
+		// following doesn't happen 
+		// (i) d does not reach n-1 
+		// (ii) (x^2) % n is not 1 
+		// (iii) (x^2) % n is not n-1 
+		while (d != n - 1) { 
+			x = (x * x) % n; 
+			d *= 2; 
+		
+			if (x == 1) 
+				return false; 
+			if (x == n - 1) 
+				return true; 
+		} 
+	
+		// Return composite 
+		return false; 
+	} 
+	
+	// It returns false if n is composite 
+	// and returns true if n is probably 
+	// prime. k is an input parameter that 
+	// determines accuracy level. Higher 
+	// value of k indicates more accuracy. 
+	static boolean isPrime(int n, int k) { 
+		
+		// Corner cases 
+		if (n <= 1 || n == 4) 
+			return false; 
+		if (n <= 3) 
+			return true; 
+	
+		// Find r such that n = 2^d * r + 1 
+		// for some r >= 1 
+		int d = n - 1; 
+		
+		while (d % 2 == 0) 
+			d /= 2; 
+	
+		// Iterate given nber of 'k' times 
+		for (int i = 0; i < k; i++) 
+			if (!miillerTest(d, n)) 
+				return false; 
+	
+		return true; 
+	} 
+	
+	// Driver program 
+	public static void main(String args[]) { 
+		
+		int k = 4; // Number of iterations 
+	
+		System.out.println("All primes smaller "
+								+ "than 100: "); 
+								
+		for (int n = 1; n < 100; n++) 
+			if (isPrime(n, k)) 
+				System.out.print(n + " "); 
+	} 
+}