77 lines
1.6 KiB
C++
77 lines
1.6 KiB
C++
#include "nth_prime.h"
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#include <cmath>
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#include <cstring>
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#include <stdexcept>
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#include <vector>
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namespace prime {
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using namespace std;
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number_t nth(size_t n, size_t sieve_size)
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{
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if (n < 1)
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throw domain_error("invalid prime number index");
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vector<number_t> primes = {2, 3, 5, 7, 11, 13};
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if (n <= primes.size())
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return primes[n - 1];
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primes.reserve(n);
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if (auto_sieve_size == sieve_size) {
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sieve_size = min(size_t(32 * 1024),
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size_t(n * (log(n) + log(log(n))) + 0.5));
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}
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vector<char> sieve(sieve_size, false);
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sieve[0] = sieve[1] = true;
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size_t first_number = 0;
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while (true) {
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for (auto p : primes) {
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size_t reminder = first_number % p;
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size_t begin = reminder ? p - reminder : 0;
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for (size_t i = begin; i < sieve_size; i += p) {
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sieve[i] = true;
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}
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}
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for (size_t i = 0; i < sieve_size; ++i) {
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if (sieve[i])
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continue;
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number_t p = first_number + i;
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primes.push_back(p);
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if (primes.size() == n)
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return p;
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for (size_t j = i; j < sieve_size; j += p) {
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sieve[j] = true;
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}
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}
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size_t next_first_number = first_number + sieve_size;
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if (next_first_number < first_number)
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throw runtime_error("failed to reach prime number");
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first_number = next_first_number;
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memset(&sieve[0], false, sieve.size()*sizeof(sieve[0]));
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}
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}
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}
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