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53 lines
1.6 KiB
Python
53 lines
1.6 KiB
Python
"""How many circular primes are there below one million?
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The number, 197, is called a circular prime because all rotations of the digits: 197, 971, and 719, are themselves prime.
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There are thirteen such primes below 100: 2, 3, 5, 7, 11, 13, 17, 31, 37, 71, 73, 79, and 97.
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How many circular primes are there below one million?
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"""
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from e007 import is_prime, prime_generator
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class NotCircular(Exception):
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pass
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def permutations(items, n):
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if n == 0:
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yield []
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else:
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for i in xrange(len(items)):
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for cc in permutations(items[:i] + items[i + 1:], n - 1):
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yield [items[i]] + cc
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def cyclic_rotation(n):
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if n < 10:
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yield n
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else:
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s = str(n)
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for i in xrange(len(s)):
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yield int(s[i:] + s[:i])
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def main():
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MAX = 1000000
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circular_primes = []
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print 'Searching for circular primes for p < {0}...'.format(MAX)
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for prime in prime_generator():
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if prime >= MAX:
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break
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try:
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# Ensure the prime *can* be circular
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if prime > 9:
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for c in [n for n in str(prime) if n not in ['1', '3', '7', '9']]:
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raise NotCircular()
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# Check all permutations
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for rotation in cyclic_rotation(prime):
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if not is_prime(rotation):
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raise NotCircular()
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circular_primes.append(prime)
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except NotCircular:
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pass
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# Clear all permutations from the list?
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print 'Circular Primes ({0}): {1}'.format(len(circular_primes), circular_primes)
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if __name__ == '__main__':
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main()
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