def is_truncatable_prime(num):
divisor = 1
for i_unused in range(10, num):
divisor *= 10
if not is_prime(num % divisor) or not is_prime(num // divisor):
return False
if len(str(divisor)) == len(str(num)):
break
return True
def get_truncatable_primes():
truncatable_primes, prime_num = [], 23
while len(truncatable_primes) < 11:
if is_prime(prime_num) and is_truncatable_prime(prime_num):
truncatable_primes.append(prime_num)
prime_num += 2
return truncatable_primes
def get_largest_pandigital_prime():
num_str = '123456789'
while True:
all_nums = sorted(get_permutations(num_str), reverse=True)
for num in all_nums:
if is_prime(int(num)):
return num
num_str = num_str[:-1]
if num_str == '': break
def quadratic_primes(num):
max_val = 0
for b in get_prime_list(num):
for a in range(-1 * (num - 1), num, 2):
n = 1
while is_prime(abs(n * n + a * n + b)):
n += 1
if n > max_val:
co_efficients, max_val = (a, b), n
return co_efficients[0] * co_efficients[1]
def get_prime_list(max_cap):
prime_nums = []
for num in range(2, max_cap + 1):
if is_prime(num):
prime_nums.append(num)
return prime_nums