C # determine whether a given large number is a prime number. The target gets the correct calculation result at a fast speed.

The title is a test question. When we see this question, the first reaction is that it is a question of procedural complexity, and the second is an algorithm problem.

Let's take a look at the rules of prime numbers:

Link: http://en.wikipedia.org/wiki/Prime_number

C # verification code:

1         public bool primeNumber(int n){2             int sqr = Convert.ToInt32(Math.Sqrt(n));3             for (int i = sqr; i > 2; i--){4                 if (n % i == 0){5                     b = false;6                 }7             }8             return b;9         }

Obviously, the Program Complexity of the above Code is N.

Let's optimize the code and then look at the following code:

 1         public bool primeNumber(int n) 2         { 3             bool b = true; 4             if (n == 2) 5                 b = true; 6             else 7             { 8                 int sqr = Convert.ToInt32(Math.Sqrt(n)); 9                 for (int i = sqr; i > 2; i--)10                 {11                     if (n % i == 0)12                     {13                         b = false;14                     }15                 }16             }17             return b;18         }

By adding a preliminary judgment, the program complexity is reduced to N/2.

The above two sections of Code determine whether a large number is correct at 100%.

1. Satisfying the large number judgment;

2. Obtain the correct results as quickly as possible;

Obviously, it is not satisfied. I checked the fastest algorithm online to get accurate results. One accepted solution is the Miller-Rabin algorithm.

Link: http://en.wikipedia.org/wiki/Miller%E2%80%93Rabin_primality_test

The basic principle of Miller-Rabin is to increase the speed (I .e., probability hit) by random number algorithm, but sacrifices the accuracy.

Miller-Rabin's judgment on the prime numbers of input large numbers is not necessarily completely accurate, but it is a basic solution for this question.

Miller-Rabin C # code:

 1 public bool IsProbablePrime(BigInteger source) { 2             int certainty = 2; 3             if (source == 2 || source == 3) 4                 return true; 5             if (source < 2 || source % 2 == 0) 6                 return false; 7  8             BigInteger d = source - 1; 9             int s = 0;10 11             while (d % 2 == 0) {12                 d /= 2;13                 s += 1;14             }15 16             RandomNumberGenerator rng = RandomNumberGenerator.Create();17             byte[] bytes = new byte[source.ToByteArray().LongLength];18             BigInteger a;19 20             for (int i = 0; i < certainty; i++) {21                 do {22                     rng.GetBytes(bytes);23                     a = new BigInteger(bytes);24                 }25                 while (a < 2 || a >= source - 2);26 27                 BigInteger x = BigInteger.ModPow(a, d, source);28                 if (x == 1 || x == source - 1)29                     continue;30 31                 for (int r = 1; r < s; r++) {32                     x = BigInteger.ModPow(x, 2, source);33                     if (x == 1)34                         return false;35                     if (x == source - 1)36                         break;37                 }38 39                 if (x != source - 1)40                     return false;41             }42 43             return true;44         }

The above are my answers to this question. You are welcome to discuss and provide better solutions.

Code Stamp: files.cnblogs.com/tmywu/PrimeNumberProject.zip