Simulation in python of the probability that two randomly chosen numbers are coprime, is close to 6 / PI^2

gistfile1.py

# Simulation created by Manuel Martinez-Almeida
# http://en.wikipedia.org/wiki/Coprime_integers

import fractions
import math
import random

def calculateProbability(end, steps):
  count = 0
	for i in range(0, steps):
		# get two random integers, from 1 to $end
		nu0 = random.randint(1, end)
		nu1 = random.randint(1, end)
		
		# increment the counter if both integers are coprimes,
		# coprimes: greatest common divisor is 1. gcd(nu0, nu1) == 1
		if fractions.gcd(nu0, nu1) == 1:
			count += 1
		
	return float(count)/steps	



# UNIT TEST
result = calculateProbability(10000000000, 1000000)
pi = math.sqrt(6 / result)
error = abs(math.pi-pi)

# SHOW RESULTS
print "Results:"
print "	Calculated: ", pi
print "	PI: ", math.pi

print "\nError:"
print "	Absolute error: ", error
print "	Relative error: ", error/math.pi