README.md

CircularPrimes

"Circular Prime" program in python

Task assumptions

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

OBJECTIVES

• 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?

Getting started

1. Find prime numbers (classic academic problem)

Sieve of Eratosthenes -> "In mathematics, the sieve of Eratosthenes is an ancient algorithm for finding all prime numbers up to any given limit."

https://en.wikipedia.org/wiki/Sieve_of_Eratosthenes

Code in python

def sieve_of_eratosthenes( number ):
 prime = [True for i in range(number + 1)]
 p = 2
 while p * p <= number:
     if prime[p]:
         for i in range(p * 2, number + 1, p):
             prime[i] = False
     p += 1
 prime[0] = False
 prime[1] = False
 for p in range(number + 1):
     if prime[p]:
         print(p)

2. Number variation without repetition (Wariacja bez powtórzeń [PL])

itertools.combinations is what I need...

https://www.kite.com/python/docs/itertools.combinations Return r length subsequences of elements from the input iterable.

this solution caused all permutations and we just needed to rearrange the numbers..

def get_iter_combinations( number ):
 str_nr = list(str(number))
 numbers = []
 for i in range(len(str_nr)):
     str_nr.append(str_nr.pop(str_nr.index(str_nr[0])))
     a = ''.join(str_nr)
     print(str_nr)
     numbers.append(a)
 print(numbers)

This solution ignores zeros and repetitions. For example: 111 or 700 -> 070, 007

2. Full Solution

def sieve_of_eratosthenes( number ):
 counter = 0
 prime = [True for i in range(number + 1)]
 p = 2
 while p * p <= number:
     if prime[p]:
         for i in range(p * 2, number + 1, p):
             prime[i] = False
     p += 1
 prime[0] = False
 prime[1] = False
 for p in range(number + 1):
     if prime[p]:
         local_counter = 0
         p_combinations = get_iter_combinations(p)
         for n in p_combinations:
             re_roll_number = int(n)
             if prime[re_roll_number]:
                 local_counter = local_counter + 1
         if local_counter == len(p_combinations):
             counter = counter + 1
 return counter


def get_iter_combinations( number ):
 str_nr = list(str(number))
 numbers = []
 for i in range(len(str_nr)):
     str_nr.append(str_nr.pop(str_nr.index(str_nr[0])))
     a = ''.join(str_nr)
     while a[:1] == '0':
         a = a[1:]
     if a in numbers:
         continue
     numbers.append(a)
 return numbers

3.Complexity

Time complexity :

O((n * log * log(n))

Memory complexity :

O(n)