58 lines
1.2 KiB
Python
58 lines
1.2 KiB
Python
'''
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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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import math
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import numpy as np
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def sieve(n):
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assert n > 1
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ns = [True] * n
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for i in range(2, math.ceil(np.sqrt(n))):
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if ns[i]:
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j = pow(i, 2)
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while j < n:
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ns[j] = False
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j = j + i
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return [i for i,val in enumerate(ns) if val][2:]
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def rotate(n):
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if n < 10:
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return n
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else:
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l = n % 10
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return l * 10**(len(str(n)) - 1) + n // 10
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def isCircular(p, primes):
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result = True
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cur = rotate(p)
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while cur != p:
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if cur not in primes:
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result = False
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break
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cur = rotate(cur)
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return result
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def main():
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print("Hello this is Patrick")
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primes = sieve(1000000)
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res = 0
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for p in primes:
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if isCircular(p, primes):
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print(p)
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res += 1
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print("Number of circular primes:", res)
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if __name__ == "__main__":
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main() |