def is_truncatable_prime(num):
num_str = str(num)
trunc_left = num_str[1:]
trunc_right = num_str[:-1]
# truncate number from ltr and rtl
# if any truncation is not prime, return false
while len(trunc_left) > 0:
if not is_prime(int(trunc_left)):
return False
trunc_left = trunc_left[1:]
while len(trunc_right) > 0:
if not is_prime(int(trunc_right)):
return False
trunc_right = trunc_right[:-1]
return True
def find_number_of_primes(a, b):
number_of_primes = 0
inp = 0
while True:
if not is_prime(inp * inp + a * inp + b):
break
inp += 1
number_of_primes += 1
return number_of_primes
def method():
print("find the largest prime factor of 600,851,475,143")
inp = 600851475143
for i in range(int(sqrt(inp)), 0, -1):
if inp % i == 0 and is_prime(i):
print(i)
break
return
def method():
print("find the 10,001st prime number")
prime_counter = 0
i = 1
while prime_counter != 10001:
i += 1
if is_prime(i):
prime_counter += 1
print(i)
return
def is_circular_prime(num_str, orig_num_str, iteration=0):
while True:
# if the num has been rotated back to the orig number without issue, return true
if iteration > 0 and num_str == orig_num_str:
return True
# get number from string and rotate number
num = int(num_str)
rotate = num_str[1:] + num_str[0]
# if iteration > 0, number has been rotated
# check if it is prime
# if true, go to next rotation
# or if this is the first iteration, we know that this number is already prime, so check next rotation
if iteration == 0 or iteration > 0 and is_prime(num):
num_str = rotate
iteration += 1
continue
# here, iteration > 0 and num is not prime, so return false
return False