From ef8cfc2d4aff680f7830d05a8f60839a5cc5a909 Mon Sep 17 00:00:00 2001
From: Philippe Zwietering <philippe.zwietering@gmail.com>
Date: Sun, 8 Nov 2020 01:57:52 +0100
Subject: [PATCH] Finally finished 26, think I did it good enough

---
 26/main.py | 86 ++++++++++++++++++++++++++++++++++++++++++++++++++----
 27/main.py |  7 +++++
 2 files changed, 88 insertions(+), 5 deletions(-)
 create mode 100644 27/main.py

diff --git a/26/main.py b/26/main.py
index e933628..3e83244 100644
--- a/26/main.py
+++ b/26/main.py
@@ -1,8 +1,84 @@
 # Find the number d < 1000 for which 1 / d has the longest recurring cycle
 # in its decimal fraction part
 
-# Observation: I first thought we only need to check prime numbers, but 
-# that is not the case. For example, 1/21 has a cycle of length 7, longer
-# than both 3 and 7, but exactly the same as the cycles of 3 and 7 combined.
-# But for 1/49 it has a cycle of length 42, so I don't think there is a
-# clever way to deduce the length of the cycles without calculating them
\ No newline at end of file
+# It seems like the cycle is never longer than the longest of the cycle length of any of its prime divisors
+# So say we want to know the length for d and d = a * b, then the cycle for d has the same length as either the cycle for a or b, whichever is longer.
+
+# So it seems we then only have to check the primes, so first let's get a prime finder in here
+
+import numpy as np
+import math
+
+def maxIndex(ns):
+	result = 0
+	m = ns[0]
+
+	for i in range(len(ns)):
+		if ns[i] > m:
+			result = i
+			m = ns[i]
+
+	return result
+
+def getPrimes(n):
+	primes = [1 for p in range(n)]
+	primes[0] = 0
+	primes[1] = 0
+
+	x = 2
+	while x < np.sqrt(n):
+		if primes[x] == 1:
+
+			for i in range(x+x, n, x):
+				primes[i] = 0
+
+		x += 1
+
+	result = []
+	for i in range(n):
+		if primes[i]:
+			result.append(i)
+
+	return result
+
+# Now we need to find out the recurring cycle length for any number
+# As a benefit for only checking prime number, we know that the cycles will always immediately start after the .'s
+
+def cycleLength(n):
+	l = int(math.log10(n)) + 1
+	y = 1
+	power = pow(10,l)
+
+	result = 1
+	
+	while True:
+
+		x = (y * power) // n
+		rest = y * power - x * n
+
+		if rest == 0:
+			return 0
+		
+		elif rest == 1:
+			break
+		
+		else:
+			y = rest
+
+		result += 1
+
+	return result * l
+
+def main():
+	print("Hello, this is Patrick")
+
+	ps = getPrimes(1000)
+	cyclelengths = [cycleLength(p) for p in ps]
+	
+	for i in range(len(ps)):
+		print(f"{ps[i]} has length: {cyclelengths[i]}")
+
+	print(f"Biggest cycle is for {ps[maxIndex(cyclelengths)]} with length {max(cyclelengths)}")
+
+if __name__ == "__main__":
+	main()
\ No newline at end of file
diff --git a/27/main.py b/27/main.py
new file mode 100644
index 0000000..3e95a24
--- /dev/null
+++ b/27/main.py
@@ -0,0 +1,7 @@
+# Quadratic primes
+
+# Consider quadratics of the form:
+# n^2 + an + b, where abs(a) < 1000 and abs(b) <= 1000
+
+# Find the product of the coefficients, a * b, for the quadratic expression that
+# produces the maximum number of primes for consecutive values of n, starting from n = 0
\ No newline at end of file