diff --git a/project_euler/problem_37/__init__.py b/project_euler/problem_37/__init__.py new file mode 100644 index 000000000000..792d6005489e --- /dev/null +++ b/project_euler/problem_37/__init__.py @@ -0,0 +1 @@ +# diff --git a/project_euler/problem_37/sol1.py b/project_euler/problem_37/sol1.py new file mode 100644 index 000000000000..c01d64d83fbe --- /dev/null +++ b/project_euler/problem_37/sol1.py @@ -0,0 +1,92 @@ +""" +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. +""" + + +from typing import List + +seive = [True] * 1000001 +seive[1] = False +i = 2 +while i * i <= 1000000: + if seive[i]: + for j in range(i * i, 1000001, i): + seive[j] = False + i += 1 + + +def is_prime(n: int) -> bool: + """ + Returns True if n is prime, + False otherwise, for 1 <= n <= 1000000 + >>> is_prime(87) + False + >>> is_prime(1) + False + >>> is_prime(25363) + False + """ + return seive[n] + + +def list_truncated_nums(n: int) -> List[int]: + """ + Returns a list of all left and right truncated numbers of n + >>> list_truncated_nums(927628) + [927628, 27628, 92762, 7628, 9276, 628, 927, 28, 92, 8, 9] + >>> list_truncated_nums(467) + [467, 67, 46, 7, 4] + >>> list_truncated_nums(58) + [58, 8, 5] + """ + str_num = str(n) + list_nums = [n] + for i in range(1, len(str_num)): + list_nums.append(int(str_num[i:])) + list_nums.append(int(str_num[:-i])) + return list_nums + + +def validate(n: int) -> bool: + """ + To optimize the approach, we will rule out the numbers above 1000, + whose first or last three digits are not prime + >>> validate(74679) + False + >>> validate(235693) + False + >>> validate(3797) + True + """ + if len(str(n)) > 3: + if not is_prime(int(str(n)[-3:])) or not is_prime(int(str(n)[:3])): + return False + return True + + +def compute_truncated_primes(count: int = 11) -> List[int]: + """ + Returns the list of truncated primes + >>> compute_truncated_primes(11) + [23, 37, 53, 73, 313, 317, 373, 797, 3137, 3797, 739397] + """ + list_truncated_primes = [] + num = 13 + while len(list_truncated_primes) != count: + if validate(num): + list_nums = list_truncated_nums(num) + if all(is_prime(i) for i in list_nums): + list_truncated_primes.append(num) + num += 2 + return list_truncated_primes + + +if __name__ == "__main__": + print(f"{sum(compute_truncated_primes(11)) = }")