Python Euler

import timeit
from primefac import primes, primefac, isprime

"==============================================="

" Largest palindrome product"
" Problem 4 "

" A palindromic number reads the same both ways. "
" The largest palindrome made from the product of two 2-digit numbers is 9009 = 91 x 99. "

" Find the largest palindrome made from the product of two 3-digit numbers. "

"==============================================="

" Solution 1"

def is_palindrome(n):
    """ReturnTrueifnisapalindrome;Falseotherwise."""
    s = str(n)
    return s == s[::-1]


def product_lst(n):
    palindrome = max_palindrome = 0
    pair = (0,0)
    for i in xrange(n - 1, 0, -1):
        "Since all palindromes are divisible by 11, either j or i has to be as well"
        if i % 11 == 0:
            j_max = i
            j_range = xrange(i+1, 0, -1)
        else:
            j_max = 11*int(i/11)
            j_range = xrange(j_max, 0, -11)

        if i*j_max < palindrome:
            break

        for j in j_range:
            product = i*j
            if product < palindrome:
                break
            if is_palindrome(product):
                if product > palindrome:
                        palindrome = product
                        pair = (i, j)
    return (pair, palindrome)


" Solution 2"


def palindrome_product(num):
    " Makes a generator that generates palindromes with length num"
    palindrome_generator = generate_palindromes(num)
    for palindrome in palindrome_generator:
        num1, num2 = is_product_of_two(palindrome, num)
        if num1 != 0:
            return ((num1, num2), palindrome)


def generate_palindromes(n):
    " Generates palindromes of decreasing order"
    first_half = 10**n - 1
    while first_half > 10**(n-1) - 1:
        second_half = str(first_half)[::-1]
        palindrome = int(str(first_half) + str(second_half))
        yield palindrome
        first_half -= 1


def is_product_of_two(palindrome, n):
    " Checks wheter the palindrome can be written as a product"
    " of two numbers of length num"
    palindrome //= 11
    "All palindromes are divisible by 11"
    num_1 = num_2 = 0
    if not isprime(palindrome):
        " Generate numbers such that 11*i has length n"
        for i in xrange(10**(n)/11, 10**(n-1)/11, -1):
            " If num2 > 10**n then num2 is no longer a n-digit number"
            if palindrome > i*10**n:
                break
            if palindrome % i == 0:
                num_1 = i*11
                num_2 = palindrome/i
                break
    return num_1, num_2


if __name__ == '__main__':

    # n = 10
    limit = 5
    print product_lst(10**limit)
    print palindrome_product(9)
    # print timeit.timeit(lambda: palindrome_product(8), number = 1)/float(1)
    # print timeit.timeit(lambda: palindrome_product(9), number = 1)/float(1)