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.