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Wednesday, 4 April 2012

Sophie Germain Prime Numbers in C++

Prime numbers are those numbers that are only divisible by 1 and themselves. Sophie geramin prime numbers are a special category of prime numbers.
By definition, a prime number, say 'p', is a sophie germain prime number if p is prime and 2p+1 is also prime. For e.g 23 is a sophie germain prime because
23 is prime and 23*2 + 1 = 47 is also prime.

For those who do not know how to check whether a number is prime or not, please read my post : Checking PRIME numbers in C++.

Now generating sophie germain primes, is actually quite a simple task. We need just need to check the following :
1 - p is prime
2 - 2p+1 is prime
3 - print p if both cases 1 and 2 turn out to be true.

The following program generates sophie germain primes upto the limit specified by the user. Please have a look at the source code to have a better
understanding of how the program works. Please leave a comment if you want to ask something or just want to say hi .

// Program to generate sophie germain prime numbers

#include <iostream>

bool checkPrime(int number)
     bool flag = true;
     if ( number == 2 ) // checks if 2 is entered(as 2 is a prime number )
      //    std::cout<<" The number is PRIME !!! ";
          return true; // terminates the program is two is enterd, as there is no need for further checking

     else // divides the number with value from 2 to (number-1)
          for (int i=2; i<number; i++)
               // if it is divisible than values smaller than number-1 it is non - prime
               if ( number%i == 0)
                    flag = false;
     return flag; // returns either true or false as the result


int main()
     int max,i = 2;
     // prompts the user to enter the max numbers to generate
     std::cout<<" Enter the max. numbers to generate : ";
     int counter = 1;

     while ( counter <= max) // run until the limit is reached
          if ( checkPrime(i) == true ) // initial check to see if p is prime
               if ( checkPrime((2*i) + 1) == true ) // secondary check to see if 2p+1 is prime
                    std::cout<<" "<<i; // displays the number if it turns out to be a sophie germain prime
     } // end of while
     std::cout<<"\n End of program !! ";
     return 0;
} // end of  main

------ OUTPUT ------

Please do comment if you don't understand any part or want to know more or just want to say thanks. I love programming and love to teach my friends. Your suggestions and appreciation will make this blog much better.   

------ Related Posts ------
1 : For more information on sophie germain primes , please visit :
3 : Generating Prime numbers in C++ :


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  2. Prime number program in C++

    prime number is only divisible by 1 and itself,
    we can easily write prime number program in c++, just check number is not divisible by any other numbers except 1 and number itself.

  3. This code is frequently ask in any examination Prime number program in C++ is very simple and easy to write. Using for loop and if else we can write this code.

  4. A prime number is a whole number greater than 1, which is only divisible by 1 and itself. First few prime numbers are : 2 3 5 7 11 13 17 19 23
    2 is the only even Prime number. Prime number program in C++. Every prime number can represented in form of 6n+1 or 6n-1, where n is natural number. 2, 3 are only two consecutive natural numbers which are prime too.


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