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

def is_prime(n):
  def prime_helper(n, x):
    if n == 1:
      return False
    elif n % x == 0:
      return False
    else:
      return prime_helper(n , x+1) if x * x <= n else True 
  return prime_helper(n, 2)

if you don't want to use a helper function

def is_prime(n, x=2):
    if n == 1:
      return False
    elif n % x == 0:
      return False
    else:
      return is_prime(n , x+1) if x * x <= n else True 

Also, you don't need to check all the numbers between (1 - N) but only up to sqrt(n). You can change your iterative approach to

for loop

from math import sqrt 
def is_prime(n):
  if n == 1:
     return False
  for i in range(2, round(sqrt(n)) + 1):
     if n % i == 0:
        return False
  return True

while loop

def is_prime(n):
  if n == 1:
    return False
  i = 2
  while i * i <= n:
     if n % i == 0:
        return False
     i += 1
  return True