Created problem_37 in project_euler

project_euler/problem_37/__init__.py

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+#

project_euler/problem_37/sol1.py

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+"""
+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)) = }")