Quick entry, posting it for safe keeping.
I've already found this useful in a few of the problems over at project euler so I figured I'd share it. Quick primes! I actually wrote this a few days ago in response to NickDMax's thread (check it out, it's pretty interesting), before I realised what he was trying to do. (I was hasty!)
This program runs in silly time, something like a tenth of a second. Not bad for finding all primes up to 100,000 and finding the nth prime number, huh?
I've already found this useful in a few of the problems over at project euler so I figured I'd share it. Quick primes! I actually wrote this a few days ago in response to NickDMax's thread (check it out, it's pretty interesting), before I realised what he was trying to do. (I was hasty!)
This program runs in silly time, something like a tenth of a second. Not bad for finding all primes up to 100,000 and finding the nth prime number, huh?
/* * A fast method of producing a table of primes * using a bitset * Author: Danny Battison */ #include <iostream> #include <bitset> #include <cmath> using namespace std; #define MAX 100000 void output(bitset<MAX> primes) { for(int i = 0; i < MAX; i++) { if(primes[i] == 1) { cout << i << " "; } } } int get_nth_prime(int n, bitset<MAX> primes) { int count = 0; for(int i = 2; i < MAX; i++) { if(primes[i]) { count++; } if(count == n) { return i; } } return 0; // could not find } int main() { bitset <MAX> primes; for(int i = 1; i < MAX; i++) { primes[i] = 1; } // quick sieve of eratosthenes -- start it off int sieve[] = {2,3,5,7}; // give it a few primes to start with for(int mul = 0; mul < 4; mul++) { for(int i = 1; i < MAX; i++) { if(i % sieve[mul] == 0 && i != sieve[mul]) { primes[i] = 0; } } } // by now, we have a list of primes with some larger numbers still left // in order to remove those, we now need to run through primes and // make sure to remove multiples of primes up to sqrt(MAX) for(int i = 2; i < sqrt(MAX); i++) { if(primes[i]) { for(int j = i+1; j < MAX; j++) { if(j % i == 0) { primes[j] = 0; } } } } cout << get_nth_prime(1000, primes); return 0; }
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