Problem:
Problem A: Sum of Consecutive Prime Numbers

Some positive integers can be represented by a sum of one or more consecutive prime numbers.
How many such representations does a given positive integer have? For example, the integer 53
has two representations 5 + 7 + 11 + 13 + 17 and 53. The integer 41 has three representations
2 + 3 + 5 + 7 + 11 + 13, 11 + 13 + 17, and 41. The integer 3 has only one representation, which is
3. The integer 20 has no such representations. Note that summands must be consecutive prime
numbers, so neither 7 + 13 nor 3 + 5 + 5 + 7 is a valid representation for the integer 20.

Your mission is to write a program that reports the number of representations for the given
positive integer.

Input

The input is a sequence of positive integers each in a separate line. The integers are between 2
and 10 000, inclusive. The end of the input is indicated by a zero.

Output

The output should be composed of lines each corresponding to an input line except the last zero.
An output line includes the number of representations for the input integer as the sum of one
or more consecutive prime numbers. No other characters should be inserted in the output.

Sample Input

2
3
17
41
20
666
12
53
0

Output for the Sample Input

1
1
2
3
0
0
1
2

Solution in Ruby (judge verdict: Accepted)

prime_array = Array.new(10001){true}
prime_array[0] = false
prime_array[1] = false
10001.times do |i|
  next unless prime_array[i]
  for j in 2..(10000 / i) do 
    prime_array[i * j] = false
  end
end
non_pure_primes = prime_array.map.with_index do |tf, i|
  i if tf
end
pure_primes = non_pure_primes.find_all{|prime| !prime.nil?}
while true
  counter = 0
  head_index = 0
  queue = [pure_primes[0]]
  given_number = gets.to_i
  break if given_number == 0
  while true
    queue_sum = queue.inject(0){|sum, number| sum + number}
    counter += 1 if queue_sum == given_number
    if queue_sum < given_number
      head_index += 1
      break if head_index == pure_primes.length
      break if pure_primes[head_index] > given_number
      queue.push(pure_primes[head_index])
    else
      queue.shift
    end
  end
  puts counter
end