ok. People concluded that there are infinitely but countably many primes.
Proof: you first construct a finite set which has 'all' primes in the world.
Then you multiply each prime and add 1 to it.
CODE: 

int len = fetch primetable.txt from ftp://International Prime Institution.net and calculate # of primes in the table;

unsigned int[] prime_set = new int[len];//let's say that len is 34253252365323

int product = 1;

for( int i=0; i    product *= prime_set[i];

}//for

product++;

if( isPrime(product) ) {

    System.out.println("IPI owned. I found new prime that doesn't belong to the primetable.txt which they say includes all primes. lol");

}//if

else {

    System.out.println("the function isPrime(int) is not working properly. lol");

}//else


And just for fun, I wrote isPriime(int) function: 

public static boolean isPrime( int p ) {

    int count = 0;

    for( int i=1; i<=Math.sqrt(p); i++ ) {

         if( p%i == 0 ) {

              count++;

          }//if

          if( count == 3 ) {//p is not prime

               return false;

          }//if

    }//for

    return true;

}//isPrime

The function is not tested...maybe it doesn't work...lol; //i'm lame

The thing is, I thought I could generate primes using the proof of infinity of # of primes.
Like: base case is "2 is prime". 2 belongs to the set of primes.
Induction: assume product of the elements in the set of primes + 1 results another prime for |set of primes| <= 1. (or >=1 i don't know...)
Current |set of primes| = 1 and 2+1 = 3 is a prime.
|set of primes| = 2 now. Let's say Set of Primes = P = { 2, 3 }
2*3+1 = 7 is a prime. P = { 2,3,7 }
2*3*7+1 = 43 is a prime!!! I thought I found something at this point...
P is now = { 2,3,7,43 }
2*3*7*43+1 = (43-1)*43+1 = 1807 is NOT a prime.
It took about 3 minuites to get 1807 on the paper ( bad arithmetician).
I thoght 1807 was a prime because it looks like it. But when I checked the web, 1807 wasn't listed as prime....
Ahhhhhh I really thought I figured something out...lol..I'm still lame.