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 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.

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

......

How to write an efficient program to check it? any clue to prove or disprove this conjecture? BTW:I asked this question at mathgroup before, but I didn't describe it clearly.