Determine pi(10^n) = pi_{k}(10^n) (for all k<=10^n)

pi.cc

// NOLINT(legal/copyright)
// g++ pi.cc -lgmp -lgmpxx -O3 -Wall -pedantic -Wextra -o pi
// (cpplinted and cppchecked)
//
#include <time.h>
#include <math.h>
#include <gmpxx.h>
#include <assert.h>

#include <iostream>
#include <cstdint>

int main(int argc, char *argv[]) {
    mpz_class mx, a = 2;
    if (argc < 2) {
        std::cerr << "Format: ./pi exp\n";
        exit(1);
    }
    uint64_t c = 0, u = atoi(argv[1]);
    mpz_ui_pow_ui(mx.get_mpz_t(), 10, u);

    do {
        mpz_nextprime(a.get_mpz_t(), a.get_mpz_t());
        ++c;
    }
    while (a <= mx);  // NOLINT
    std::cerr << "pi(" << mx << ")=" << c << "\n";

    return 0;
}

Determining $pi(10^n)$ with GMP lib sequentially in AMD 7950X CPU (with boost frequency 5.5GHz):

hermann@7950x:~/RSA_numbers_factored/c++$ time ./pi 8
pi(100000000)=5761455

real	0m8.068s
user	0m8.065s
sys	0m0.001s
hermann@7950x:~/RSA_numbers_factored/c++$ time ./pi 9
pi(1000000000)=50847534

real	1m21.527s
user	1m21.523s
sys	0m0.001s
hermann@7950x:~/RSA_numbers_factored/c++$ time ./pi 10
pi(10000000000)=455052511

real	15m16.745s
user	15m16.704s
sys	0m0.001s
hermann@7950x:~/RSA_numbers_factored/c++$ 

Matches table values here:
https://en.wikipedia.org/wiki/Prime-counting_function#Table_of_%CF%80(x),_%E2%81%A0x/log_x_%E2%81%A0,_and_li(x)

$pi(10^{10}) = pi_{k}(10^{10}) = 455,052,511 &lt; 614,983,774 = pi_{k^2+(k+1)^2}(10^{10})$, see
https://gist.github.com/Hermann-SW/94241e719dd3518a3276d804b627319d?permalink_comment_id=5928968#gistcomment-5928968

Above gist code is outperformed by simple sieve of Eratosthenes.
But GMP code does not need big memory, while sieve code does.

hermann@7950x:~/RSA_numbers_factored/c++$ time ./pi_ 8
5761455

real	0m0.735s
user	0m0.699s
sys	0m0.036s
hermann@7950x:~/RSA_numbers_factored/c++$ time ./pi_ 9
50847534

real	0m10.186s
user	0m9.879s
sys	0m0.306s
hermann@7950x:~/RSA_numbers_factored/c++$ time ./pi_ 10
455052511

real	1m51.612s
user	1m48.876s
sys	0m2.728s
hermann@7950x:~/RSA_numbers_factored/c++$ 

$ cat pi_.cc 
// NOLINT(legal/copyright)
// g++ pi_.cc -O3 -Wall -pedantic -Wextra -o pi_
// (cpplinted and cppchecked)
//
#include <string.h>

#include <iostream>
#include <cassert>

char *V;
typedef __int64_t num;

int main(int argc, char *argv[]) {
    assert(argc == 2);
    assert(atoi(argv[1]) >= 2);
    num mx = 1;
    for (int e = 1; e <= atoi(argv[1]); ++e) {
      mx *= 10;
    }

    V = new char[1 + mx];
    assert(V);
    explicit_bzero(V, 1+mx);

    num c = 0;
    for (num i = 2; i <= mx; ++i) {
      if (V[i] != 0)  continue;

      for (num j = 2*i; j <= mx; j += i)  V[j] = 1;
      ++c;
    }

    std::cout << c << "\n";

    return 0;
}
$