坎宁安链

坎宁安链是质数的序列。它有2种类型：

• 第一种坎宁安链：它是长度为n的质数序列，如下所述：

  Let p1, p2, p3, …., p_n be a cunningham chain of length n than
  p₂ = 2*p₁ + 1
  p₃ = 4*p₁ + 3
  p₄ = 8*p₁ + 7
  . . .
  . . .
  p_n = 2^n-1*p1 + (2^n-1 – 1)

  这里的p1，p2，p3，….，pn都是质数。如果p的任何值不是非质数，则链终止于它之前的数字。

  对于p0 = 2，序列将为2 5 11 23 47

  下面是上述的实现：

  C++

  // C++ program for cunningham chain
  // Function to print the series
  // of first kind
  #include 
    
  using namespace std;
    
  // Function to print
  // Cunningham chain of the first kind
  void print(int p0)
  {
      int p1, i = 0, x, flag, k;
    
      // Iterate till all elements
      // are printed
      while (1) {
          flag = 1;
          x = (int)(pow(2, i));
          p1 = x * p0 + (x - 1);
    
          // check prime or not
          for (k = 2; k < p1; k++) {
              if (p1 % k == 0) {
                  flag = 0;
                  break;
              }
          }
          if (flag == 0)
              break;
          printf("%d ", p1);
          i++;
      }
  }
    
  // Driver Code
  int main()
  {
      int p0 = 2;
      print(p0);
    
      return 0;
  }

  Java

  // Java Program to print the 
  // series of first kind
  class GFG
  {
    
  // Function to print
  // Cunningham chain
  // of the first kind
  static void print(int p0)
  {
      int p1, i = 0, x, flag, k;
    
      // Iterate till all 
      // elements are printed
      while (true)
      {
          flag = 1;
          x = (int)(Math.pow(2, i));
          p1 = x * p0 + (x - 1);
    
          // check prime or not
          for (k = 2; k < p1; k++) 
          {
              if (p1 % k == 0)
              {
                  flag = 0;
                  break;
              }
          }
          if (flag == 0)
              break;
          System.out.print(" " + p1);
          i++;
      }
  }
    
  // Driver Code
  public static void main(String args[])
  {
      int p0 = 2;
      print(p0);
  }
  }
    
  // This code is contributed
  // by Kirti_Mangal

  Python3

  # Python3 program for cunningham chain 
    
  # Function to print Cunningham chain 
  # of the first kind 
  def print_C(p0):
        
      i = 0;
        
      # Iterate till all elements
      # are printed
      while(True):
          flag = 1;
          x = pow(2, i);
          p1 = x * p0 + (x - 1);
            
          # check prime or not
          for k in range(2, p1):
              if (p1 % k == 0):
                  flag = 0;
                  break;
            
          if (flag == 0):
              break;
            
          print(p1, end = " ");
          i += 1; 
    
  # Driver Code 
  p0 = 2; 
  print_C(p0); 
    
  # This code is contributed by mits

  C#

  // C# Program to print the 
  // series of first kind
  using System;
  class GFG
  {
    
  // Function to print
  // Cunningham chain
  // of the first kind
  static void print(int p0)
  {
      int p1, i = 0, x, flag, k;
    
      // Iterate till all 
      // elements are printed
      while (true)
      {
          flag = 1;
          x = (int)(Math.Pow(2, i));
          p1 = x * p0 + (x - 1);
    
          // check prime or not
          for (k = 2; k < p1; k++) 
          {
              if (p1 % k == 0)
              {
                  flag = 0;
                  break;
              }
          }
          if (flag == 0)
              break;
          Console.Write(" " + p1);
          i++;
      }
  }
    
  // Driver Code
  public static void Main()
  {
      int p0 = 2;
      print(p0);
  }
  }
    
  // This code is contributed
  // by Akanksha Rai(Abby_akku)

  ---

  ---

  输出：

  2 5 11 23 47
  

• 第二类坎宁安链：它是长度为n的质数序列，如下所述：

  Let p1, p2, p3, …., p_n be a cunningham chain of length n than
  p₂ = 2*p₁ – 1
  p₃ = 4*p₁ – 3
  p₄ = 8*p₁ – 7
  . . .
  . . .
  p_n = 2^n-1*p1 – (2^n-1 – 1)

  对于p0 = 19，该序列将为19、37、73。

  下面是上述的实现：

  C++

  // C++ program for cunningham chain
  // Function to print the series
  // of second kind
  #include 
    
  using namespace std;
    
  // Function to print
  // Cunningham chain of the second kind
  void print(int p0)
  {
      int p1, i = 0, x, flag, k;
    
      // Iterate till all elements
      // are printed
      while (1) {
          flag = 1;
          x = (int)(pow(2, i));
          p1 = x * p0 - (x - 1);
    
          // check prime or not
          for (k = 2; k < p1; k++) {
              if (p1 % k == 0) {
                  flag = 0;
                  break;
              }
          }
          if (flag == 0)
              break;
          printf("%d ", p1);
          i++;
      }
  }
    
  // Driver Code
  int main()
  {
      int p0 = 19;
      print(p0);
    
      return 0;
  }
  

  Java

  // Java program for cunningham chain 
  // Function to print the series 
  // of second kind 
    
  class GFG{
        
  // Function to print Cunningham chain
  //  of the second kind 
  static void print(int p0) 
  { 
      int p1, i = 0, x, flag, k; 
    
      // Iterate till all elements 
      // are printed 
      while (true) 
      { 
          flag = 1; 
          x = (int)(Math.pow(2, i)); 
          p1 = x * p0 - (x - 1); 
    
          // check prime or not 
          for (k = 2; k < p1; k++)
          { 
              if (p1 % k == 0) 
              { 
                  flag = 0; 
                  break; 
              } 
          } 
          if (flag == 0) 
              break; 
          System.out.print(p1+" "); 
          i++; 
      } 
  } 
    
  // Driver Code 
  public static void main(String[] args) 
  { 
      int p0 = 19; 
      print(p0); 
  } 
  }
    
  // This code is contributed by mits
  

  Python3

  # Python3 program for cunningham chain 
    
  # Function to print Cunningham chain
  # of the second kind 
  def print_t(p0): 
    
      i = 0;
    
      # Iterate till all elements 
      # are printed 
      while (True): 
          flag = 1; 
          x = pow(2, i); 
          p1 = x * p0 - (x - 1); 
    
          # check prime or not 
          for k in range(2, p1): 
              if (p1 % k == 0): 
                  flag = 0; 
                  break; 
    
          if (flag == 0): 
              break; 
          print(p1,end=" "); 
          i+=1; 
    
  # Driver Code 
  p0 = 19; 
  print_t(p0); 
    
  # This code is contributed by mits
  

  C＃

  // C# program for cunningham chain 
  // Function to print the series 
  // of second kind 
  using System;
  class GFG
  {
        
  // Function to print 
  // Cunningham chain of the second kind 
  static void print(int p0) 
  { 
      int p1, i = 0, x, flag, k; 
    
      // Iterate till all elements 
      // are printed 
      while (true) 
      { 
          flag = 1; 
          x = (int)(Math.Pow(2, i)); 
          p1 = x * p0 - (x - 1); 
    
          // check prime or not 
          for (k = 2; k < p1; k++)
          { 
              if (p1 % k == 0)
              { 
                  flag = 0; 
                  break; 
              } 
          } 
          if (flag == 0) 
              break; 
          Console.Write(p1 + " "); 
          i++; 
      } 
  } 
    
  // Driver Code 
  static void Main() 
  { 
      int p0 = 19; 
      print(p0); 
  } 
  }
    
  // This code is contributed by mits
  

  输出：

  19 37 73