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@@ -0,0 +1,49 @@
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+from math import sqrt
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+
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+def prime(n):
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+ """Returns a boolean indicating whether an integer is a prime"""
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+ if n <= 1:
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+ return False
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+ for i in range(2, int(sqrt(n) + 1)):
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+ if n % i == 0:
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+ return False
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+ return True
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+
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+def upright(d):
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+ return 4*d**2-10*d+7
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+def upleft(d):
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+ return 4*d**2-8*d+5
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+def downleft(d):
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+ return 4*d**2-6*d+3
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+def downright(d):
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+ return 4*d**2-4*d+1
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+
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+def percentPrimeSpiral(sideLen):
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+ diagonalLen = (sideLen+1)/2
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+ totalDiagonals = (diagonalLen-1)*4 + 1
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+
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+ numPrimes = 0
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+ for i in range(1,diagonalLen+1):
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+ if prime(upright(i)):
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+ numPrimes += 1
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+ if prime(upleft(i)):
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+ numPrimes += 1
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+ if prime(downright(i)):
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+ numPrimes += 1
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+ if prime(downleft(i)):
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+ numPrimes += 1
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+ return numPrimes / float(totalDiagonals)
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+
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+def main():
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+ primeRatio = .99
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+ sideLen = 1001
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+
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+ while primeRatio > 0.12:
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+ primeRatio = percentPrimeSpiral(sideLen)
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+ sideLen += 10
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+ print primeRatio
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+
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+ print sideLen
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+ print primeRatio
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+
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+main()
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