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49 lines
1.6 KiB
Python
49 lines
1.6 KiB
Python
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"""Investigate the number of primes that lie on the diagonals of the spiral grid.
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Starting with 1 and spiralling anticlockwise in the following way, a square spiral with side length 7 is formed.
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37 36 35 34 33 32 31
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38 17 16 15 14 13 30
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39 18 5 4 3 12 29
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40 19 6 1 2 11 28
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41 20 7 8 9 10 27
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42 21 22 23 24 25 26
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43 44 45 46 47 48 49
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It is interesting to note that the odd squares lie along the bottom right diagonal, but what is more interesting is that 8 out of the 13 numbers lying along both diagonals are prime; that is, a ratio of 8/13 62%.
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If one complete new layer is wrapped around the spiral above, a square spiral with side length 9 will be formed. If this process is continued, what is the side length of the square spiral for which the ratio of primes along both diagonals first falls below 10%?
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"""
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from e007 import is_prime
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def spiral_corners_generator():
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n = 1
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size = 1
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while True:
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corners = []
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if size == 1:
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yield [1]
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else:
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for i in range(4):
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n = n + (size - 1)
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corners.append(n)
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yield corners
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size = size + 2
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def main():
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size = 1
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diagonals = 0
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primes = 0
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for corners in spiral_corners_generator():
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diagonals = diagonals + len(corners)
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primes = primes + len([c for c in corners if is_prime(c)])
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pct = primes / float(diagonals) * 100
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if size > 7 and pct < 10.0:
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break
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size = size + 2
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print 'Side Length: {0}, Percentage: {1}'.format(size, pct)
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if __name__ == '__main__':
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main()
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