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unknownnick

prime numbers

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I don''t know if this has anything to do with games, but... I have an algorithm for searching prime numbers... the code would look like this
  
#include <windows.h>
#include <math.h>
#include <iostream>
using namespace std;

int n=0;
int x=3;

bool us_prime(int number) 
{ 
  int max_number = (int)(sqrt(number)+0.5); 
  int i = 3; 

  if (number % 2 == 0) 
   return false; 

  while (i<max_number) 
  { 
   if (number % i == 0) 
     return false; 
   i += 2; 
  } 
  return true; 
} 

int main(){
	
	cin >> n;

	for(x; x<n; x+=2){
		if(is_prime(x))
			cout << x << endl;
	}

	cin >> n;

	return 0;
}
  
I hope it''ll work. And now the question. Can anyone find me even faster way of searching them?

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Well... this technique isn''t anything new. The original algo doesn''t have that "0.5" in it though, as far as i remember.. cuz itz not necessary.

I saw some indian guys coming up with a faster technique few months back and the doc wos posted somewhere here in gamedev.... SEARCH SEARCH !

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Every prime is 6n+/-1 for some natural number n except for 2 and 3, but every 6n+/-1 is not prime. You can use that to further reduce the numbers you check. For instance it would eliminate 9, 15 and 21. So step by six starting at 5 and check two numbers per pass through the loop. That way you only check 1/3 of the numbers instead of 1/2 of them. You could also use 30n+/-7, 30n+/-11 and 30+/-13, but that gets a little cumbersome and only reduces it to 1/5 from 1/3.

Hum, I guess that is a bigger reduction than from 1/2 to 1/3, but it is still cumbersome.

[edited by - LilBudyWizer on November 3, 2002 7:44:51 PM]

Hehe, well, I guess you might want to include 30n+/-1 in there if you wanted it to be right which makes it 8/30=4/15 instead of 1/5 which means you only reduced it by 1/5 by using 30 versus 6.

[edited by - LilBudyWizer on November 3, 2002 7:56:21 PM]

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quote:
Original post by browny
I saw some indian guys coming up with a faster technique few months back and the doc wos posted somewhere here in gamedev.... SEARCH SEARCH !


Actually, while the algorithm they discovered indeed runs in polynomial time, it is still slower than the algorithms developed today because it requires a very large-ordered polynomial.

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The Sieve of Eratosthenes is sort of interesting to program... give it a try if you haven''t already!

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