# 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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