32 lines
917 B
Python
32 lines
917 B
Python
#!/usr/bin/env python3
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# We shall say that an n-digit number is pandigital if it makes use of all the digits 1 to n exactly once. For example, 2143 is a 4-digit pandigital
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# and is also prime.
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#
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# What is the largest n-digit pandigital prime that exists?
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from projecteuler import is_pandigital, is_prime, timing
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@timing
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def p041() -> None:
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# 8- and 9-digit pandigital numbers can't be prime, because
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# 1+2+...+8=36, which is divisible by 3, and 36+9=45 which is
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# also divisible by 3, and therefore the whole number is divisible
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# by 3. So we can start from the largest 7-digit pandigital number,
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# until we find a prime.
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i = 7654321
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while i > 0:
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if is_pandigital(i, len(str(i))) and is_prime(i):
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break
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# Skipping the even numbers.
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i = i - 2
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print('Project Euler, Problem 41')
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print(f'Answer: {i}')
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if __name__ == '__main__':
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p041()
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