88 lines
2.2 KiB
Python
88 lines
2.2 KiB
Python
"""
|
|
The number 3797 has an interesting property.
|
|
Being prime itself, it is possible to continuously remove digits from left to right,
|
|
and remain prime at each stage: 3797, 797, 97, and 7.
|
|
Similarly we can work from right to left: 3797, 379, 37, and 3.
|
|
|
|
Find the sum of the only eleven primes that are both truncatable from left to right and right to left.
|
|
|
|
NOTE: 2, 3, 5, and 7 are not considered to be truncatable primes.
|
|
"""
|
|
|
|
import time
|
|
from itertools import product
|
|
|
|
|
|
def timer(func):
|
|
def wrapper(*args, **kwargs):
|
|
start_time = time.time()
|
|
result = func(*args, **kwargs)
|
|
end_time = time.time()
|
|
print(f"Time taken: {end_time - start_time:.6f} seconds")
|
|
return result
|
|
|
|
return wrapper
|
|
|
|
|
|
def combine_lists(a: list[int], b: list[int | None], c: list[int]) -> list[int]:
|
|
"""将三个列表的每个元素组合成数字"""
|
|
return [int(f"{x}{y}{z}") for x, y, z in product(a, b, c)]
|
|
|
|
|
|
def is_prime(n: int) -> bool:
|
|
"""判断一个数是否为素数"""
|
|
if n < 2:
|
|
return False
|
|
for i in range(2, int(n**0.5) + 1):
|
|
if n % i == 0:
|
|
return False
|
|
return True
|
|
|
|
|
|
def truncate_left(n: int) -> bool:
|
|
"""从左到右截断一个数"""
|
|
length = len(str(n))
|
|
while n > 0:
|
|
if not is_prime(n):
|
|
return False
|
|
n %= 10 ** (length - 1)
|
|
length -= 1
|
|
return True
|
|
|
|
|
|
def truncate_right(n: int) -> bool:
|
|
"""从右到左截断一个数"""
|
|
while n > 0:
|
|
if not is_prime(n):
|
|
return False
|
|
n //= 10
|
|
return True
|
|
|
|
|
|
def TruncatablePrime() -> list[int]:
|
|
begin = [2, 3, 5, 7]
|
|
end = [3, 7]
|
|
middle = [1, 3, 7, 9]
|
|
res = []
|
|
for length in range(2, 7):
|
|
if length - 2 == 0:
|
|
midb = []
|
|
else:
|
|
midb = product(middle, repeat=length - 2)
|
|
midb = [int("".join(map(str, x))) for x in midb]
|
|
nums = combine_lists(begin, midb, end)
|
|
for num in nums:
|
|
if is_prime(num):
|
|
if truncate_left(num) and truncate_right(num):
|
|
res.append(num)
|
|
return res
|
|
|
|
|
|
@timer
|
|
def main():
|
|
print(sum(TruncatablePrime()))
|
|
|
|
|
|
if __name__ == "__main__":
|
|
main()
|