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058.py
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058.py
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#!/usr/bin/env python
"""
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%?
"""
__author__ = "Julia Schwarz"
from primes import primesfrom2to
primes = set(primesfrom2to(10**9))
pct = 1.0
level = 1
diagonals = [1]
num_primes = 0
print "level, side_length, n_diagonals, n_primes, pct"
while pct >= 0.1:
side_length = 2 * level + 1
square = side_length ** 2
for i in xrange(4):
corner = square - (side_length - 1) * i
diagonals.append(corner)
if corner in primes:
num_primes += 1
pct = float(num_primes) / len(diagonals)
print level, side_length, len(diagonals), num_primes, pct, max(diagonals)
level += 1
print max(primes)