GoldConjecture | Topcoder Archive

Problem Statement

A famous mathematical conjecture states that all numbers greater than 5 can be expressed as the sum of 3 prime numbers. A number is prime if it is only evenly divisible by itself and 1. Furthermore, 2 is the lowest prime number. Given an integer k greater than 5, you will return the 3 prime numbers whose sum is k in increasing order. If there is more than one combination of three primes whose sum is k return the 3 primes with the highest product (i.e., the three primes multiplied together produces the highest value).

Definition

Class:: GoldConjecture
Method:: numbers
Parameters:: int
Returns:: int[]
Method signature:: int[] numbers(int k)
(be sure your method is public)

Constraints

k will be between 6 and 2000 inclusive
All given values of k will have solutions

Examples

```
10
```
```
Returns: { 2,  3,  5 }
```
2,3,5 is the only solution that works.
```
12
```
```
Returns: { 2,  5,  5 }
```
2,3,7 and 2,5,5 both are primes that add up to 12 but: 2*3*7 = 42 2*5*5 = 50 So the solution is {2,5,5}
```
2000
```
```
Returns: { 2,  977,  1021 }
```
```
1997
```
```
Returns: { 659,  661,  677 }
```
```
777
```
```
Returns: { 257,  257,  263 }
```
```
6
```
```
Returns: { 2,  2,  2 }
```

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