Efficiently check if two numbers are co-primes (relatively primes)?

Question

What is the most efficient ("pythonic") way to test/check if two numbers are co-primes (relatively prime) in Python.

For the moment I have this code:

def gcd(a, b):
    while b != 0:
        a, b = b, a % b
    return a

def coprime(a, b):
    return gcd(a, b) == 1

print(coprime(14,15)) #Should be true
print(coprime(14,28)) #Should be false

Can the code for checking/testing if two numbers are relatively prime be considered "Pythonic" or there is some better way?

Solution

The only suggestion for improvement might be with your function gcd. Namely, you could use gcd that's defined in math (for Python 3.5) for a speed boost.

Defining coprime2 that uses the built-in version of gcd:

from math import gcd as bltin_gcd

def coprime2(a, b):
    return bltin_gcd(a, b) == 1

You almost cut down execution speed by half due to the fact that math.gcd is implemented in C (see math_gcd in mathmodule.c):

%timeit coprime(14, 15)
1000000 loops, best of 3: 907 ns per loop

%timeit coprime2(14, 15)
1000000 loops, best of 3: 486 ns per loop

For Python <= 3.4 you could use fractions.gcd but, as noted in a comment by @user2357112, it is not implemented in C. Actually, there's really no incentive to actually use it, its implementation is exactly the same as yours.

Comments

[user2357112]

There isn't nearly as much of a benefit on pre-3.5, though, since fractions.gcd was written in Python instead of C.

[İbrahim İpek]

Old question but math module functions in Python usually are no good for big numbers. It may crash. I would go for something like SymPy or PARI/GP