Estimate Erastosthenes Sieve size required to find I-th prime number

eratosthenes_sieve_size.py

import math

def sieve_size_bytes(number_bits):
  max_index = 2**number_bits
  max_prime = max_index * math.log(max_index)
  number_bytes = (number_bits) + 7) / 8
  sieve_size = long(math.sqrt(max_prime) * number_bytes / 3)
  return sieve_size

print("size for 32-bit index: " + str(sieve_size_bytes(32)))
print("size for 64-bit index: " + str(sieve_size_bytes(64)))

# Outputs:
# size for 32-bit index: 411534
# size for 64-bit index: 76283622977