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35 lines
1.4 KiB
Python
35 lines
1.4 KiB
Python
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"""Find the sum of all eleven primes that are both truncatable from left to right and right to left.
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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.
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Find the sum of the only eleven primes that are both truncatable from left to right and right to left.
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NOTE: 2, 3, 5, and 7 are not considered to be truncatable primes.
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"""
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from e007 import is_prime, prime_generator
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def is_truncatable(prime):
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if prime < 10:
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return False
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rtl = [int(str(prime)[:i]) for i in xrange(len(str(prime))) if i > 0 and i < len(str(prime))]
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ltr = [int(str(prime)[i:]) for i in xrange(len(str(prime))) if i > 0 and i < len(str(prime))]
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truncated = sorted(rtl + ltr, reverse=True)
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for n in truncated:
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if not is_prime(n):
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return False
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print 'OK', prime, rtl, ltr
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return True
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def main():
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truncatable = []
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generator = prime_generator()
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print 'Searching for truncatable primes...'
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while len(truncatable) < 11:
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prime = generator.next()
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if is_truncatable(prime):
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truncatable.append(prime)
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print 'Found {0} truncatable primes'.format(len(truncatable))
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print 'Sum:', sum(truncatable)
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if __name__ == '__main__':
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main()
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