Denote P[n]$P[n]$ as the prime sequence {$p_1,p_2,\cdots,p_n$}$\{p_1,p_2,\cdots,p_n\}$.
Conjecture:When n=2k+1 is odd, prime list P[n] can be partitioned to two non-overlapping sublists , each sublist has equal sum Total[P[n]]/2;When n=2k is even, prime list P[n] can be partitioned to 2 non-overlapping sublists , one sublist's sum is (Total[P[n]]-1)/2, the other's is (Total[P[n]]+1)/2.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:
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
..... $$ \begin{align*} 3-2 &= 1 \\ 5-3-2 &= 0 \\ 7 - 5 - 3 + 2 &= 1 \\ 11 - 7 - 5 + 3 - 2 &= 0 \\ 13 - 11 - 7 + 5 + 3 - 2 &= 1 \end{align*} $$ and so on.
How tocould I write an efficient program to check it? any clueAny clues to prove or disprove this conjecture? BTW
BTW:I I asked this question at mathgroup before, but I didn't describe it clearly.
