Prime Counting Function

primecounting.py

def primepi(limit):
  def Prime_sieve(n): #Sieve of Eratosthenes
    result = [True] * (n + 1)
    result[0] = result[1] = False
    for i in range(int(math.sqrt(n)) + 1):
      if result[i]:
        for j in range(2 * i, len(result), i):
          result[j] = False
    return result
  
  prime_gen = Prime_sieve(limit + 50)
  primes = [x for x in range(len(prime_gen)) if prime_gen[x]]
  array = [0]*(limit+1)
  p_index = 0
  for x in range(1, limit + 1):
      while True:
          if primes[p_index] > x:
              array[x] = p_index
              break
          p_index += 1
  return array