Denote $P[n]$ as the prime sequence $\{p_1,p_2,\cdots,p_n\}$.

**Conjecture:**

* When $n=2k+1$ is odd, prime list $P[n]$ can be partitioned into two non-overlapping sublists, in which each sublist has equal sum $\operatorname{Total}[P[n]]/2$.
* When $n=2k$ is even, prime list $P[n]$ can be partitioned into two non-overlapping sublists, one sublist's sum is $(\operatorname{Total}[P[n]]-1)/2$, the other's is $(\operatorname{Total}[P[n]]+1)/2$.

For example:
$$
\begin{align*}
3-2 &= 1 \\
5-3-2 &= 0 \\
7 - 5 - 3 + 2 &= 1 \\
11 - 7 - 5 + 3 - 2 &= 0 \\
13 - 11 - 7 + 5 + 3 - 2 &= 1
\end{align*}
$$
and so on.

How could I write an efficient program to check it? Any clues to prove or disprove this conjecture?

BTW: I asked this question at mathgroup before, but I didn't describe it clearly.