Cunningham chain

A Cunningham chain is a sequence of prime numbers. It is of 2 types:

• Cunningham chain of the first kind: It is a sequence of prime numbers of length n described as below :

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

Here p1, p2, p3, …., pn are all prime numbers. If any value of p comes out to be non-prime than chain ends at the number which came before it.

for p0 = 2, the sequence will be 2 5 11 23 47

Below is the implementation of the above:

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)

PHP



Output:

2 5 11 23 47

• Cunningham chain of the second kind: It is a sequence of prime numbers of length n described as below:

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

for p0 = 19, the sequence will be 19, 37, 73.

Below is the implementation of the above:

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

PHP



Output:

19 37 73

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