From 305251d5331b9b0ea713c86e7d95778f0e306a6c Mon Sep 17 00:00:00 2001 From: Correl Roush Date: Wed, 5 May 2010 05:23:31 +0000 Subject: [PATCH] Problem 058 git-svn-id: file:///srv/svn/euler@72 e5f4c3ec-3c0c-11df-b522-21efaa4426b5 --- e058.py | 49 +++++++++++++++++++++++++++++++++++++++++++++++++ 1 file changed, 49 insertions(+) create mode 100644 e058.py diff --git a/e058.py b/e058.py new file mode 100644 index 0000000..602d454 --- /dev/null +++ b/e058.py @@ -0,0 +1,49 @@ +"""Investigate the number of primes that lie on the diagonals of the spiral grid. + +Starting with 1 and spiralling anticlockwise in the following way, a square spiral with side length 7 is formed. + + 37 36 35 34 33 32 31 + 38 17 16 15 14 13 30 + 39 18 5 4 3 12 29 + 40 19 6 1 2 11 28 + 41 20 7 8 9 10 27 + 42 21 22 23 24 25 26 + 43 44 45 46 47 48 49 + +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%. + +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%? +""" + +from e007 import is_prime + +def spiral_corners_generator(): + n = 1 + size = 1 + while True: + corners = [] + if size == 1: + yield [1] + else: + for i in range(4): + n = n + (size - 1) + corners.append(n) + yield corners + size = size + 2 + +def main(): + size = 1 + diagonals = 0 + primes = 0 + for corners in spiral_corners_generator(): + diagonals = diagonals + len(corners) + primes = primes + len([c for c in corners if is_prime(c)]) + pct = primes / float(diagonals) * 100 + if size > 7 and pct < 10.0: + break + size = size + 2 + + print 'Side Length: {0}, Percentage: {1}'.format(size, pct) + +if __name__ == '__main__': + main() \ No newline at end of file