 # C++ Programming Code Examples

## C++ > Data Structures and Algorithm Analysis in C++ Code Examples

### Randomized primality testing algorithm, with a test program

``` Randomized primality testing algorithm, with a test program #include <iostream.h> #include "Random.h" typedef int HugeInt; /** * Method that implements the basic primality test. * If witness does not return 1, n is definitely composite. * Do this by computing a^i (mod n) and looking for * non-trivial square roots of 1 along the way. */ HugeInt witness( const HugeInt & a, const HugeInt & i, const HugeInt & n ) { if( i == 0 ) return 1; HugeInt x = witness( a, i / 2, n ); if( x == 0 ) // If n is recursively composite, stop return 0; // n is not prime if we find a non-trivial square root of 1 HugeInt y = ( x * x ) % n; if( y == 1 && x != 1 && x != n - 1 ) return 0; if( i % 2 != 0 ) y = ( a * y ) % n; return y; } /** * The number of witnesses queried in randomized primality test. */ const int TRIALS = 5; /** * Randomized primality test. * Adjust TRIALS to increase confidence level. * n is the number to test. * If return value is false, n is definitely not prime. * If return value is true, n is probably prime. */ bool isPrime( const HugeInt & n ) { Random r; for( int counter = 0; counter < TRIALS; counter++ ) if( witness( r.randomInt( 2, (int) n - 2 ), n - 1, n ) != 1 ) return false; return true; } int main( ) { for( int i = 101; i < 200; i += 2 ) if( isPrime( i ) ) cout << i << " is prime" << endl; return 0; } ``` 