Pi Approximating by Monte Carlo method

pi-approximator.py

#
# The probability that two integers randomly chosen are primes between then
# is surprisingly related to pi, this probability value is equal to 6/pi**2.
# This was discovered by Cesaro, in 1883.
# This code uses Monte Carlo method to test 10**7 pairs of random integers between
# 1 and 10**10 to approximate numerically the value of pi.
#

from math import sqrt      # square root (to calculate pi from pi**2)
from fractions import gcd  # greatest common division (to test for primality between integers)
from random import randint # yields a random integer between a range

# increment this numbers to get more accurate pi approximations
TESTS = 10**7 # number of Monte Carlo tests to perform
MAX = 10**10  # size of the uniform random integer space to sample

print sqrt( 6.*TESTS /
            sum(1 for n in xrange(TESTS) if
                gcd(randint(1,MAX),
                    randint(1,MAX)) == 1))

Reference: http://en.wikipedia.org/wiki/Pi#Number_theory_and_Riemann_zeta_function