How do I find a prime number using recursion in Python

Question

I have to find out whether number(N) is a prime or not using recursion, no loops are allowed. I\'ve tried converting the usual code that uses a for loop to a recursive one,

Answer 1

Your function sometimes returns something and sometimes returns nothing -- it should be either all one or the other, not both. In this case is_prime() looks like a boolean function so it should return True or False. We'll leave the printing to the caller:

def is_prime(N, a=3):

    if N == 2:  # special case
        prime = True
    elif N <= 1 or N % 2 == 0:  # too small or even
        prime = False
    elif a * a > N:  # tried all divisors to sqrt, must be prime
        prime = True
    elif (N % a) == 0:  # divides evenly, not a prime
        prime = False
    else:  # can't tell yet, recursively try the next (odd) divisor
        prime = is_prime(N, a+2)

    return prime

for x in range(100):
    if is_prime(x):
        print(x)

Keep it simple. Think through each possible case. Avoid increasing the indention depth unnecessarily, it makes your code more complicated.

The above solution tries to speed up prime detection by avoiding even numbers (both divisor and number) and limiting the divisor to the square root of the number. This can matter as without these optimizations, a recursive solution will likely run out of call stack space at around N=1,000 whereas the above should go to N=1,000,000 without expanding the call stack.