# Commits

committed e227940

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• Parent commits bea9f1f

# File problems/problem51.py

` 		return v in self.primes`
` `
` def run():`
`+	"""`
`+	Soooo...`
`+`
`+	We can narrow down the prime selecting process based on the divisble-by-three`
`+	principle (that is, that if the sum of the digits of a number is divisible by`
`+	three then the number is divisible by three).`
`+`
`+	That helps because any number that is divisible by three is not prime (that is,`
`+	any number but three itself).`
`+`
`+  The following are charts over the first few n replaced digits.  The chart marks`
`+	an X where the sum will be a 3.  The last column shows the number of possible`
`+	primes for this permutation.  Using the charts I will show that you can only`
`+	ever have an 8 prime family when n is a multiple of three.`
`+`
`+	Y axis is sum of other digits mod 10.`
`+`
`+  Chart for 1 * replaced digits.`
`+  =================================`
`+     Sum of replaced digits`
`+		 0  1  2  3  4  5  6  7  8  9    Max`
`+  0  X        X        X        X  | 6`
`+	1        X        X        X     | 6`
`+	2     X        X        X        | 6`
`+	3  X        X        X        X  | 6`
`+	4  `
`+	5  ... pattern continues`
`+	6`
`+`
`+  Chart for 2 * replaced digits.`
`+  =================================`
`+     Sum of replaced digits`
`+		0x2 1x2 2x2 3x2 4x2 5x2 6x2 7x2 8x2 9x2`
`+		 0   2   4   6   8   1   3   5   7   9    Max`
`+  0  X           X           X           X  | 6`
`+	1      X           X           X          | 7`
`+	2          X           X           X      | 7`
`+	3  X           X           X           X  | 6`
`+	4  `
`+	5  ... pattern continues`
`+	6`
`+	7`
`+	8`
`+	9`
`+`
`+  Chart for 3 * replaced digits.`
`+  =================================`
`+     Sum of replaced digits`
`+		0x3 1x3 2x3 3x3 4x3 5x3 6x3 7x3 8x3 9x3`
`+		 0   3   6   9   3   6   9   3   6   9    Max`
`+  0  X   X   X   X   X   X   X   X   X   X  | 0`
`+	1                                         | 9`
`+	2                                         | 9`
`+	3  X   X   X   X   X   X   X   X   X   X  | 0`
`+	4  `
`+	5  ... pattern continues`
`+	6`
`+`
`+  Chart for 4 * replaced digits.`
`+  =================================`
`+     Sum of replaced digits`
`+		0x4 1x4 2x4 3x4 4x4 5x4 6x4 7x4 8x4 9x4`
`+		 0   4   8   3   7   2   6   1   5   9    Max`
`+  0  X           X           X           X  | 6`
`+	1          X           X           X      | 6`
`+	2      X           X           X          | 6`
`+	3  X           X           X           X  | 6`
`+	4  `
`+	5  ... pattern continues`
`+	6`
`+	7`
`+`
`+	"""`
` 	p = SievedPrimes()`
` 	p.is_prime(100000)`
` 	return 0`