# Java Program to Implement Miller Rabin Primality Test

This is a Java Program to Implement Miller Rabin Primality Test Algorithm. Miller Rabin Primality Test is an algorithm which is used to determine if a given number is prime or not.

Here is the source code of the Java Program to Implement Miller Rabin Primality Test Algorithm. The Java program is successfully compiled and run on a Windows system. The program output is also shown below.

1. `/**`
2. ` ** Java Program to Implement Miller Rabin Primality Test Algorithm`
3. ` **/`
4. ` `
5. `import java.util.Scanner;`
6. `import java.util.Random;`
7. `import java.math.BigInteger;`
8. ` `
9. `/** Class MillerRabin **/`
10. `public class MillerRabin`
11. `{`
12. `    /** Function to check if prime or not **/`
13. `    public boolean isPrime(long n, int iteration)`
14. `    {`
15. `        /** base case **/`
16. `        if (n == 0 || n == 1)`
17. `            return false;`
18. `        /** base case - 2 is prime **/`
19. `        if (n == 2)`
20. `            return true;`
21. `        /** an even number other than 2 is composite **/`
22. `        if (n % 2 == 0)`
23. `            return false;`
24. ` `
25. `        long s = n - 1;`
26. `        while (s % 2 == 0)`
27. `            s /= 2;`
28. ` `
29. `        Random rand = new Random();`
30. `        for (int i = 0; i < iteration; i++)`
31. `        {`
32. `            long r = Math.abs(rand.nextLong());            `
33. `            long a = r % (n - 1) + 1, temp = s;`
34. `            long mod = modPow(a, temp, n);`
35. `            while (temp != n - 1 && mod != 1 && mod != n - 1)`
36. `            {`
37. `                mod = mulMod(mod, mod, n);`
38. `                temp *= 2;`
39. `            }`
40. `            if (mod != n - 1 && temp % 2 == 0)`
41. `                return false;`
42. `        }`
43. `        return true;        `
44. `    }`
45. `    /** Function to calculate (a ^ b) % c **/`
46. `    public long modPow(long a, long b, long c)`
47. `    {`
48. `        long res = 1;`
49. `        for (int i = 0; i < b; i++)`
50. `        {`
51. `            res *= a;`
52. `            res %= c; `
53. `        }`
54. `        return res % c;`
55. `    }`
56. `    /** Function to calculate (a * b) % c **/`
57. `    public long mulMod(long a, long b, long mod) `
58. `    {`
59. `        return BigInteger.valueOf(a).multiply(BigInteger.valueOf(b)).mod(BigInteger.valueOf(mod)).longValue();`
60. `    }`
61. `    /** Main function **/`
62. `    public static void main (String[] args) `
63. `    {`
64. `        Scanner scan = new Scanner(System.in);`
65. `        System.out.println("Miller Rabin Primality Algorithm Test\n");`
66. `        /** Make an object of MillerRabin class **/`
67. `        MillerRabin mr = new MillerRabin();`
68. `        /** Accept number **/`
69. `        System.out.println("Enter number\n");`
70. `        long num = scan.nextLong();`
71. `        /** Accept number of iterations **/`
72. `        System.out.println("\nEnter number of iterations");`
73. `        int k = scan.nextInt();`
74. `        /** check if prime **/`
75. `        boolean prime = mr.isPrime(num, k);`
76. `        if (prime)`
77. `            System.out.println("\n"+ num +" is prime");`
78. `        else`
79. `            System.out.println("\n"+ num +" is composite");`
80. ` `
81. `    }`
82. `}`

```Miller Rabin Primality Algorithm Test

Enter number

5510389

Enter number of iterations
2

5510389 is prime```

Sanfoundry Global Education & Learning Series – 1000 Java Programs. 