Meissel–Mertens constant: Difference between revisions

=={{header|C++}}==

<syntaxhighlight lang="c++">

#include <cmath>

#include <cstdint>

#include <iomanip>

#include <iostream>

#include <vector>

std::vector<double> list_prime_reciprocals(const int32_t& limit) {

const int32_t half_limit = ( limit % 2 == 0 ) ? limit / 2 : 1 + limit / 2;

std::vector<bool> composite(half_limit);

for ( int32_t i = 1, p = 3; i < half_limit; p += 2, ++i ) {

if ( ! composite[i] ) {

for ( int32_t a = i + p; a < half_limit; a = a + p ) {

composite[a] = true;

}

}

}

std::vector<double> result(composite.size());

result[0] = 0.5;

for ( int32_t i = 1, p = 3; i < half_limit; p += 2, ++i ) {

if ( ! composite[i] ) {

result.emplace_back(1.0 / p);

}

}

return result;

}

int main() {

std::vector<double> prime_reciprocals = list_prime_reciprocals(100'000'000);

const double euler = 0.577'215'664'901'532'861;

double sum = 0.0;

for ( double reciprocal : prime_reciprocals ) {

sum += reciprocal + log(1.0 - reciprocal);

}

const double meissel_mertens = euler + sum;

std::cout << "The Meissel-Mertens constant = " << std::setprecision(8) << meissel_mertens << std::endl;

}

</syntaxhighlight>

{{ out }}

<pre>

The Meissel-Mertens constant = 0.26149721

</pre>