A solution to the ZeroCater math-y challenge that is capable of finding the fifth clean chain of primes.

clean_chain.rb

# Take a sequence of N numbers. We'll call the sequence a "Clean Chain of length N" 
# if the sum of the first N - 1 numbers is evenly divisibly by the Nth number.

# For example, the sequence [2, 4, 6, 8, 10] forms a clean chain of length 5, 
# since 2 + 4 + 6 + 8 = 20, which is divisible by 10, and the sequence has 5 numbers.

# The first clean chain formed out of the sequence of primes is simply [2], with length 1.
# The second is [2, 3, 5] with length 3.
# The third is [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 
# 53, 59, 61, 67, 71], with length 20

# To use CleanChain, initialize it with the location of a file or files containing
# the numbers that will form the chain.

# x = CleanChain.new("../numbers/numbers_file.txt")

# Then call chain_length with an argument of which chain number you want to find

# x.chain_length(3)
# => 20

# Alternatively, chain_length will return 
# "A longer list of numbers is required to find chain #{nth_chain}"
# if that is the case

class CleanChain
  attr_reader :prime_array

	def initialize( directory )
		@prime_array = create_prime_array( directory )
	end

	def create_prime_array( directory )
		prime_text = ""
		Dir.glob(directory).each do |primes|
			prime_text << open( primes, 'r' ).lines.drop(1).join(' ')
		end

		prime_array = []
		prime_text.split.each do |number|
			prime_array << number.to_i
		end
		prime_array
	end

	def chain_length ( nth_chain )
		chain_counter = 0
		sum = 0

		@prime_array.each_with_index do |number, index|
			sum += number
			chain_counter += 1 if ( sum % number ).zero?
		  return @prime_array.index(number) + 1 if chain_counter == nth_chain
		end
		"A longer list of numbers is required to find chain #{nth_chain}"
	end
end

# Note: downloaded the first 50 million primes from http://primes.utm.edu/lists/small/millions/
# This makes it possible to find the fifth clean chain in a reasonable timeframe

x = CleanChain.new("./primes*.txt")

puts x.chain_length(4)