While loops with multiple condtions. Python

Question

I'm writing a function that, given a random int, will return the next int that is both a prime number and a palindrome. ie getint(13) will return 101. One of the conditions of this function is that recursion is not allowed.

Where am i going wrong here?

def golf(number):
    x = number +1
    for i in range(2, x):
        while str(x) != str(x)[::-1] and  x % i == 0:
            x += 1
    return x

Answer 1

Your for loop will only go as far as x 's initial value: the range(2,x) is computed only once, right after x = number + 1 . So increasing x inside the loop doesn't make a difference. Consider using a while loop, something like:

i = 2
while i <= x:
    ...
    i += 1

And you should probably first check is x is a palindrome (a "cheap" operation) and then, if it is, check weather it is prime (an "expensive" operation), not try do it all in a couple of nested loops that make little sense.

Answer 2

Divide the problem into smaller pieces. It will be easier for you to understand what's going on:

def golf(number):
    x = number + 1
    while True:
        if is_palindrome(x) and is_prime(x):
            return x
        x += 1

Now all you have to do is implement is_palindrome(x) and is_prime(x) :

import math

def is_prime(x):
    for i in xrange(2, math.ceil(math.sqrt(x))+1):
        if x % i == 0:
            return False
    return True

def is_palindrome(x):
    x = str(x)
    return x == x[::-1]

Side note : the math.ceil(math.sqrt(x))+1 might be an overkill (perhaps int(...)+1 is enough) if math.sqrt works correctly for squares (ie does not depend on floating point calculations so math.sqrt(a*a)==a is always true). Well in worst case the loop will do one more iteration then necessary. Better safe then sorry.

Answer 3

In your code:

def golf(number):
    x = number +1
    for i in range(2, x):
        while str(x) != str(x)[::-1] and  x % i == 0:
            x += 1
    return x

The program execution will not satisfy the while loop half of the time since any even number will not be divisible by any odd number and vice-versa . Also in a single iteration of the for loop, x will be incremented every time the while loop is satisfied.

You need to separate the prime checking and palindrome checking. The approach given by freakish is the simplest.