Only complete nthCircularPrime. assume all other methods are implemented correct

Question

Only complete nthCircularPrime. assume all other methods are implemented correctly. Do not use string indexing, lists, or recursion in this assignment. Python languange

2. nthCircularPrime [70 pts] A circular prime is an integer number with the property that any rotation of that number's digits is prime. In this case, rotation refers to cycling the digits of a number; for example, the rotations of 1234 are 1234, 2341, 3412, and 4123. You can read more about this on the Wikipedia page. Single-digit primes are all circular, of course. To find the nth circular prime, you'll need to write isPrime and three other functions: 1. rotateNumber [20 pts] number's digits by one would turn the number 1234 to 4123. 2. isCircularPrime [30 pts] This function takes a non-negative integer number, x, and determines whether that number is a circular prime. To do this, you'll need to check whether every rotation of the number is prime. 3. nthCircularPrime [20 pts] This function takes a non-negative integer number n, and returns the nth circular prime.

Explanation / Answer

def isPrime(n):
    if (n < 2):
        return False
    if (n == 2):
        return True
    if (n % 2 == 0):
        return False
    maxFactor = round(n**0.5)
    for factor in range(3,maxFactor+1,2):
        if (n % factor == 0):
            return False
    return True

def digCount(x):
    count = 0
    while (x >= 10):
        x //= 10
        count += 1
    return count

def rotateNumber(x):
    numDigits = digCount(x)
    lastDigit = x % 10
    first = (x - lastDigit) / 10
    last = lastDigit * 10**numDigits
    return last + first

def isCircularPrime(x):
    for i in range(digCount(x)+1):
        #print(x)
        if (not isPrime(x)):
            return False
        x = rotateNumber(x)
    return True

def nthCircularPrime(n):
    if n >= 0:
       num = 2
       count = 0;
       while count < n:
           num = num + 1
           if isCircularPrime(num):
              #print(count,num)
              count = count + 1
       return num
    else:
       print("Invalid argument")
       return -1

#print(isPrime(32))
#print(isCircularPrime(23))
#print(rotateNumber(23))

print(nthCircularPrime(4))  
print(nthCircularPrime(5))  
print(nthCircularPrime(11))
print(nthCircularPrime(15))
print(nthCircularPrime(25))

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