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# 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.
##### Analysis
Because the program needs to deal with consecutive prime numbers for each test case, and the upper limit of prime numbers is 10,000, the offline method can be used to solve the problem. First, all prime numbers less than 10,001 are obtained and stored in list prime[1 .. total] in ascending order. Then we deal with the test cases one by one.

Source: ACM Japan 2005.

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Solution submitted by Dzeng at May 7, 2020, 11:20 p.m.
def get_primes(): data_list = [i for i in range(2, 10001)] primes = [] while len(data_list) > 0: primes.append(data_list[0]) for l in data_list: if l % primes[len(primes)-1] == 0: data_list.remove(l) return primes def get_sum_of_prime(n, primes): start = 0 currentsum = 0 outputtotal = 0 while primes[start] <= n: for i in range(start, len(primes)): currentsum += primes[i] if currentsum == n: outputtotal += 1 break elif currentsum > n: break start += 1 currentsum = 0 return outputtotal a_list = [i for i in range(2, 10001)] primes = get_primes() #listtocheck = input("enter numbers; end number with;") inputlist = listtocheck.split(";") for i in a_list: print(get_sum_of_prime(int(i), primes))

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