Toy script to create a RSA key from scratch

rsakey.py

__author__ = 'cdumitru'

from Crypto.PublicKey import RSA
from Crypto import Random
import gmpy
import base64


#tup (tuple) - A tuple of long integers, with at least 2 and no more than 6 items. The items come in the following order:
#RSA modulus (n).
#Public exponent (e).
#Private exponent (d)
#First factor of n (p).
#Second factor of n (q)

n = 0L
p = 0L
q = 0L
e = 65537L

string_to_be_encrypted="Hello"

phi = (p - 1) * (q - 1)
d = long(gmpy.invert(e, phi))

tup = (n ,e, d, p, q )
key = RSA.construct(tup)

random_generator = Random.new().read
data = key.encrypt(string_to_be_encrypted,random_generator)


print key.exportKey('PEM')
print key.publickey().exportKey()
print base64.b64encode(data[0])

How does it work
????