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 Rust (judge verdict: Accepted)

extern crate core;

use std::fmt;
use std::cmp::{Ordering, min, max};
use std::fmt::{Display, Error, Formatter, Binary};
use std::f32::MAX;
use std::ops::{Add, Sub, Mul, Div, Neg, Index, IndexMut};
use std::collections::{BTreeMap, VecDeque, BinaryHeap, BTreeSet};

fn show<T: Display>(vec: &Vec<T>) {
    if vec.is_empty() {
        println!("[]");
    }else {
        print!("[{}", vec[0]);
        for i in 1 .. vec.len() {
            print!(", {}", vec[i]);
        }
        println!("]");
    }
}
fn show2<T: Display>(vec: &Vec<Vec<T>>) {
    if vec.is_empty() {
        println!("[]");
    }else {
        for l in vec {
            show(l);
        }
    }
}
macro_rules! read_line{
    () => {{
        let mut line = String::new();
        std::io::stdin().read_line(&mut line).ok();
        line
    }};
    (delimiter: ' ') => {
        read_line!().split_whitespace().map(|x|x.to_string()).collect::<Vec<_>>()
    };
    (delimiter: $p:expr) => {
        read_line!().split($p).map(|x|x.to_string()).collect::<Vec<_>>()
    };
    (' ') => {
        read_line!(delimiter: ' ')
    };
    ($delimiter:expr) => {
        read_line!(delimiter: $delimiter)
    };
    (' '; $ty:ty) => {
        read_line!().split_whitespace().map(|x|x.parse::<$ty>().ok().unwrap()).collect::<Vec<$ty>>()
    };
    ($delimiter:expr; $ty:ty) => {
        read_line!($delimiter).into_iter().map(|x|x.parse::<$ty>().ok().unwrap()).collect::<Vec<$ty>>()
    };
}
macro_rules! read_value{
    () => {
        read_line!().trim().parse().ok().unwrap()
    }
}
macro_rules! let_all {
    ($($n:ident:$t:ty),*) => {
        let line = read_line!(delimiter: ' ');
        let mut iter = line.iter();
        $(let $n:$t = iter.next().unwrap().parse().ok().unwrap();)*
    };
}
macro_rules! let_mut_all {
    ($($n:ident:$t:ty),*) => {
        let line = read_line!(delimiter: ' ');
        let mut iter = line.iter();
        $(let mut $n:$t = iter.next().unwrap().parse().ok().unwrap();)*
    };
}
fn primes(upper_limit: usize) -> Vec<i32> {
    let mut is_prime = vec![true; upper_limit + 1];
    let mut i = 4;
    while i <= upper_limit {
        is_prime[i] = false;
        i += 2;
    }
    i = 3;
    while i <= upper_limit {
        if is_prime[i] {
            let mut j = i * i;
            while j <= upper_limit {
                is_prime[j] = false;
                j += i;
            }
        }
        i += 2;
    }
    let mut result = Vec::new();
    for i in 2 .. is_prime.len() {
        if is_prime[i] {
            result.push(i as i32);
        }
    }
    result
}
fn main() {
    let mut prime = primes(10000);
    for i in 1 .. prime.len() {
        prime[i] += prime[i - 1];
    }
    loop {
        let_all!(n: i32);
        if n == 0 {
            return
        }
        let mut count = 0;
        for &to in &prime {
            if (to > n && prime.binary_search(&(to - n)).is_ok()) || (n == to) {
                count += 1
            }
        }
        println!("{}", count);
    }
}