2010-05-05 14:37:51 +00:00
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"""What is the largest n-digit pandigital prime that exists?
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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 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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from e007 import is_prime
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from e035 import permutations
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def pandigital_prime_generator(n):
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2010-05-05 14:38:33 +00:00
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if n not in [3, 7, 9]:
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2010-05-05 14:37:51 +00:00
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raise Exception('Invalid pandigital prime length')
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for end in [3, 7, 9]:
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digits = range(1, n + 1)
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if end not in digits:
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continue
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digits.remove(end)
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for start in sorted(permutations(digits, len(digits)), reverse=True):
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number = int(''.join([str(i) for i in start] + [str(end)]))
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if is_prime(number):
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yield number
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def main():
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for len in [9, 7, 3]:
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for n in sorted(pandigital_prime_generator(len), reverse=True):
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print 'Pandigital Prime:', n
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return
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if __name__ == '__main__':
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main()
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