"""Circular primes

Problem 35

The number, 197, is called a circular prime because all rotations of the digits: 197, 971, and 719, are themselves prime.

There are thirteen such primes below 100: 2, 3, 5, 7, 11, 13, 17, 31, 37, 71, 73, 79, and 97.

How many circular primes are there below one million?"""

from typing import List, Tuple, Iterator, Generator

from itertools import permutations

from utils import isPrime

def digit_rotations(number: int) -> Iterator[int]:

digits = [digit for digit in str(number)]

perms = (int("".join(digits[i:] + digits[:i])) for i in range(len(digits)))

return perms

print("The digit rotations of 1234 are:")

print(list(digit_rotations(1234)))

print("The digit rotations of 12311 are:")

print(list(digit_rotations(12311)))

def nextprime() -> Iterator[int]:

number += 1

def isCircularPrime(number: int) -> bool:

return True

assert isCircularPrime(1) == False

assert isCircularPrime(2) == True

assert isCircularPrime(19937) == True

assert isCircularPrime(23) == False

primes: Iterator[int] = nextprime()

iprime: int = next(primes)

count: int = 0

while iprime <= 1_000_000:

if isCircularPrime(iprime):

count += 1

iprime = next(primes)

print(f"The number of circular primes is {count}")