62 lines
1.1 KiB
C++
62 lines
1.1 KiB
C++
#include "nth_prime.h"
|
|
|
|
#include <cstring>
|
|
#include <iostream>
|
|
#include <stdexcept>
|
|
#include <vector>
|
|
|
|
|
|
namespace prime {
|
|
|
|
using namespace std;
|
|
|
|
number_t nth(size_t n)
|
|
{
|
|
if (n < 1)
|
|
throw domain_error("invalid prime index");
|
|
|
|
vector<number_t> primes = {2, 3, 5, 7, 11, 13};
|
|
primes.reserve(n - 1);
|
|
|
|
static const size_t sieve_size = 32*1024;
|
|
|
|
bool sieve[sieve_size] = {0};
|
|
sieve[0] = sieve[1] = true;
|
|
|
|
size_t page = 0;
|
|
|
|
while (primes.size() < n - 1) {
|
|
|
|
for (auto p : primes) {
|
|
|
|
size_t start = ((page*sieve_size + p - 1)/p)*p
|
|
- page*sieve_size;
|
|
|
|
for (size_t i = start; i < sieve_size; i += p) {
|
|
|
|
sieve[i] = true;
|
|
}
|
|
}
|
|
|
|
for (size_t i = 0; i < sieve_size; ++i) {
|
|
|
|
if (sieve[i])
|
|
continue;
|
|
|
|
number_t p = page*sieve_size + i;
|
|
primes.push_back(p);
|
|
|
|
for (size_t j = i; j < sieve_size; j += p) {
|
|
|
|
sieve[j] = true;
|
|
}
|
|
}
|
|
|
|
memset(sieve, 0, sieve_size);
|
|
++page;
|
|
}
|
|
|
|
return primes[n - 1];
|
|
}
|
|
|
|
}
|