Problem 058

git-svn-id: file:///srv/svn/euler@72 e5f4c3ec-3c0c-11df-b522-21efaa4426b5

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()