C # obtain all the prime numbers in the screening range,

C # obtain all the prime numbers in the screening range,

   
Popular Science: screening is a simple algorithm for prime number verification. It is said to be Eratosthenes of ancient Greece, around 274-BC ~ Invented in 194, also known as the sieve of Eratosthenes method ).
 

   
To be honest, I used to verify whether a certain number is a prime number in the case of qualitative quantity. I can easily draw a conclusion by using definition. The Code is as follows:
 

   
01: public static bool IsPrime (int n) 02: {// determine whether n is a prime number 03: if (n <2) return false; 04: for (int I = n-1; I> 1; I --) 05: {// n divided by each natural number greater than 1, which is smaller than n 06: if (n % I = 0) 07: {// if divisible, it is not a prime number 08: return false; 09:} 10 :} // otherwise, it indicates the prime number 11: return true; 12 :}

  
However, if we use this method to determine all the prime numbers between two numbers x and y, We need to judge them cyclically:

  
1:  for (int i = x; i < y; i++)2:  {3:      if (IsPrime(i))4:      {5:          Console.Write(i);6:      }7:  }

  
Today, I accidentally saw that the screening method may be more suitable for solving such problems-finding all the prime numbers within a certain upper limit:

  
01:  private static List<int> GenPrime(int j)02:  {03:      List<int> ints=new List<int>();04:      BitArray bts=new BitArray(j+1);05:      for (int x = 2; x < bts.Length / 2; x++)06:      {07:          for (int y = x + 1; y < bts.Length; y++)08:          {09:              if (bts[y] == false && y % x == 0)10:              {11:                  bts[y] = true;12:              }13:          }14:      }15:      for (int x = 2; x < bts.Length; x++)16:      {17:          if (bts[x] == false)18:          {19:              ints.Add(x);20:          }21:      }22:      return ints;23:  }

  
However, if the prime number in the range is required, the difference set of the two ranges must be required:

  
1:  List<int> ListResult = GenPrime(x).Except(GenPrime(y)).ToList();

  
Then I found a linear screening algorithm in another blog. I changed it to C # code:

  
01:  private static List<int> GenPrime1(int x)02:  {03:      int num_prime = 0;04:      List<int> ints = new List<int>();05:      BitArray isNotPrime = new BitArray(x);06:      for (int i = 2; i < x; i++)07:      {08:          if (!isNotPrime[i])09:          {10:              ints.Add(i);11:              num_prime++;12:          }       13:          for (int j = 0; j < num_prime && i * ints[j] < x; j++)14:          {15:              isNotPrime[i * ints[j]] = true;16:              if (!Convert.ToBoolean(i % ints[j]))                  17:                  break;18:          }19:      }20:      return ints;21:  }

  
Sent to the original post: prime number obtained by ordinary sieve + fast linear sieve

  
PS. I wrote a blog for the first time. If there are any deficiencies, please let me know. I must change it!