Question

I can’t figure out why this python function returns None if it calls itself recursively.

It was part of my solution to a Project Euler problem. I have solved the problem in a better way anyhow, but this is still annoying me as the function seems to work OK – and it seems to know the value of the variable I wanted to return.

def next_prime(previous):
    if previous % 2 == 0:
        candidate = previous + 1
    else:
    candidate = previous + 2
    print "trying", candidate
    prime = True
    for div in range(2,candidate//2,1):
        if candidate % div == 0:
            prime = False
            print candidate, "is not prime - divisible by", div
            next_prime(candidate)
            break
    if prime is True:
        print candidate, "is prime"
        #return candidate

last = 896576
print "After", last, ", the next prime is..."
next_prime(last)

This gives:

After 896576 , the next prime is...
trying 896577
896577 is not prime - divisible by 3
trying 896579
896579 is not prime - divisible by 701
trying 896581
896581 is not prime - divisible by 7
trying 896583
896583 is not prime - divisible by 3
trying 896585
896585 is not prime - divisible by 5
trying 896587
896587 is prime

But if I uncomment the return statement it only returns a value if the first try is prime, otherwise it returns None.

Answer 1

You forgot to return a value when there is failure to find a prime:

for div in range(2,candidate//2,1):
    if candidate % div == 0:
        prime = False
        print candidate, "is not prime - divisible by", div
        return next_prime(candidate)

Recursion isn’t really suitable here though. It isn’t much more elegant than the simple iterative approach. Also, you could overflow the stack if you hit an area where there are lot of non-primes between two consecutive primes.