Project Euler Problem 35

Project 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?

# 1百万以下有多少环形素数？

思路：要是环形素数，必须由1379构成（2，5除外）

def struct(n):
    string = '1379'
    result = []
    if n == 0:
        return ' '
    for i in string:
        for j in struct(n-1):
            temp = i + j
            result.append(temp.strip())
    return result

def change(string):
    lst = [string]
    for i in range(1,len(string)):
        substr = string[i:] + string[:i]
        lst.append(substr)
    return lst

def isprime(n):
    if n <= 1:
        return False
    for i in range(2,int(n**0.5+1)):
        if n % i == 0:
            return False
    return True


lst2 = [2,5]     # 2, 5 特殊
for i in range(1,7):   # 最大6位数
    for j in struct(i):
        for s in change(j):
            if not isprime(int(s)):
                break
        else:
            lst2.append(int(j))

# lst 的长度就是个数