#apery.py
#probability that 3 integers have no factors in common (i.e. they are relatively prime) is 1/Apery
# Apery's constant 1.2020569031...  sum of i^-3  (1+1/2^3+1/3^3+1/4^3...)
# sum of the inverses of the cubes of the positive integers is irrational.
#reciprocal is .83190737...

import random

def apery(n):
    '''calculate Apery's constant, sum of 1/ i^3  with n terms'''
    apery_sum = 0
    for i in range(1,n+1):
        apery_sum += 1 / i**3
    return apery_sum

places = int(input("Enter number of terms to calculate Apery's constant to: "))
print(apery(places))


def euclid(a, b):
    if b > a:
        a,b = b,a    #swap so a>b
    	
    while b > 0:
        r = a % b
        a = b
        b = r
    	
    return a

        
trials = int(input("Enter number of trials of random triples: "))
max_int = int(input("Enter max int: "))
triplesThatHaveCommonFactors = 0

for i in range(trials):
    a = random.randint(1,max_int)
    b = random.randint(1,max_int)
    c = random.randint(1,max_int)
    #print(a,b,c)
    if euclid(a,b)>1 and euclid(a,c)>1 and euclid(b,c)>1 :  # not relatively prime
        triplesThatHaveCommonFactors += 1

print(1- triplesThatHaveCommonFactors/trials)

sum_i_minus3 = 0
for i in range(1,100):
    sum_i_minus3 += 1/i**3
print("sum_i_minus3: ",sum_i_minus3)
print("1/sum_i_minus3:",1/sum_i_minus3)