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54 lines
1.4 KiB
Python
54 lines
1.4 KiB
Python
from itertools import permutations
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from math import sqrt
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from typing import List
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"""
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We shall say that an n-digit number is pandigital if it makes use of all the digits
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1 to n exactly once. For example, 2143 is a 4-digit pandigital and is also prime.
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What is the largest n-digit pandigital prime that exists?
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"""
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"""
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All pandigital numbers except for 1, 4 ,7 pandigital numbers are divisible by 3.
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So we will check only 7 digit panddigital numbers to obtain the largest possible
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pandigital prime.
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"""
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def is_prime(n: int) -> bool:
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"""
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Returns True if n is prime,
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False otherwise.
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>>> is_prime(67483)
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False
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>>> is_prime(563)
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True
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>>> is_prime(87)
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False
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"""
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if n % 2 == 0:
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return False
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for i in range(3, int(sqrt(n) + 1), 2):
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if n % i == 0:
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return False
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return True
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def compute_pandigital_primes(n: int) -> List[int]:
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"""
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Returns a list of all n-digit pandigital primes.
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>>> compute_pandigital_primes(2)
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[]
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>>> max(compute_pandigital_primes(4))
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4231
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>>> max(compute_pandigital_primes(7))
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7652413
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"""
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pandigital_str = "".join(str(i) for i in range(1, n + 1))
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perm_list = [int("".join(i)) for i in permutations(pandigital_str, n)]
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return [num for num in perm_list if is_prime(num)]
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if __name__ == "__main__":
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print(f"{max(compute_pandigital_primes(7)) = }")
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