Circular Primes (Project Euler #35)

def isPrime(p):
    if primes[len(primes) - 1] ** 2 < p:
        print("Error: Attempted to prime check a number with an improper prime list!")
        return False

    for q in primes:
        if q**2 > p:
            return True

        if not p % q:
            return False

def checkRotations(p):
    s = str(p)
    rotations = len(s) - 1

    for r in range(rotations):
        s += s[0]
        s = s[1:]

        if not isPrime(int(s)):
            return False

    return True

primes = [2]
p = 3
n = 1
show = False

try:
    ceiling = int(input("Enter an upper bound for searching for primes: "))
except ValueError:
    print("Error: Not a natural number!")
    exit()

if str(input("Enable individual printout? [Y/n]: ")).upper() == "Y":
    show = True

if show:
    print(primes[0], end = "\t")

while p < ceiling:
    if isPrime(p):
        primes.append(p)
        n += 1

        if show:
            print(str(p), end = "\t")
            if not n % 10:
                print()

    p += 2

print("\n" + str(len(primes)) + " primes found overall.")

c = 0

for p in primes:
    if checkRotations(p):
        if show:
            print(p, "is a circular prime.")

        c += 1

print(c, "circular primes found overall.")