output_description: 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.
input_description: 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.
attempt: p = []
  a = [0] * 2 + [1] * 10001
  for i in range(2, int(10000**0.5) + 1):
      if a[i]:
          for j in range(i * i, 10001, i):
              a[j] = 0
  for i in range(2, 10001):
      if a[i]:
          p += [i]
  b = [0] * 5736397
  for i in range(len(p)):
      c = 0
      for j in range(i, len(p)):
          c += p[j]
          b[c] += 1
  while 1:
      n = int(input())
      if n == 0:
          break
      print(b[n])
  
problem_description: 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.
samples: [{"input": "3\n    17\n    41\n    20\n    666\n    12\n    53\n    0", "output": "1\n    2\n    3\n    0\n    0\n    1\n    2"}]