66 lines
1.7 KiB
Python
66 lines
1.7 KiB
Python
#!/usr/bin/python3
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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,
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# 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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#
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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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#
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# NOTE: 2, 3, 5, and 7 are not considered to be truncatable primes.
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from timeit import default_timer
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from projecteuler import is_prime
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def is_tr_prime(n):
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# One-digit numbers and non-prime numbers are
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# not truncatable primes.
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if n < 11 or not is_prime(n):
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return False
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tmp = n // 10
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# Remove one digit at a time from the right and check
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# if the resulting number is prime. Return 0 if it isn't.
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while tmp > 0:
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if not is_prime(tmp):
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return False
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tmp = tmp // 10
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# Starting from the last digit, check if it's prime, then
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# add back one digit at a time on the left and check if it
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# is prime. Return 0 when it isn't.
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i = 10
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tmp = n % i
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while tmp != n:
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if not is_prime(tmp):
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return False
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i = i * 10
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tmp = n % i
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# If it gets here, the number is truncatable prime.
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return True
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def main():
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start = default_timer()
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i = 0
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n = 1
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sum_ = 0
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# Check every number until 11 truncatable primes are found.
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while i < 11:
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if is_tr_prime(n):
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sum_ = sum_ + n
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i = i + 1
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n = n + 1
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end = default_timer()
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print('Project Euler, Problem 37')
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print('Answer: {}'.format(sum_))
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print('Elapsed time: {:.9f} seconds'.format(end - start))
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if __name__ == '__main__':
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main()
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