Formulas for segmenting Gourdon's A formula about primecount HOT 4 CLOSED

  uint64_t min_index_1st_prime = pi[x_star] + 1;
  uint64_t min_1st_prime = primes[min_index_1st_prime];

  // x / (primes[i] * primes[i+1]) >= low
  // primes[i] * primes[i+1] <= x / low
  // primes[i] < sqrt(x / low)
  // primes[i+1] <= sqrt(x / low) || primes[i+1] >= sqrt(x / low)
  uint64_t x_div_low = x / low;
  uint64_t sqrt_low = min(isqrt(x_div_low), x13);
  uint64_t max_index_1st_prime = pi[sqrt_low];
  if (primes[max_index_1st_prime] < max_prime &&
      primes[max_index_1st_prime] * primes[max_index_1st_prime+1] > x_div_low)
    max_index_1st_prime -= 1;

  uint64_t min_2nd_prime = min(x / (high * primes[b]), max_prime);
  uint64_t min_index_2nd_prime = pi[min_2nd_prime] + 1;
  min_index_2nd_prime = max(min_index_2nd_prime, b + 1);
  min_2nd_prime = primes[min_index_2nd_prime];

  uint64_t max_2nd_prime = min(x / (low * primes[b]), isqrt(x / primes[b]));
  uint64_t max_index_2nd_prime = pi[max_2nd_prime];

x / (primes[b] * primes[q]) >= x^(1/3)

min_index_1st_prime = pi[x_star] + 1;
high = x / (primes[min_index_1st_prime] * primes[min_index_1st_prime+1]) + 1