Partition prime list into equal k sublists. How to write code for

*To*: mathgroup at smc.vnet.net*Subject*: [mg107000] Partition prime list into equal k sublists. How to write code for*From*: a boy <a.dozy.boy at gmail.com>*Date*: Sun, 31 Jan 2010 05:57:05 -0500 (EST)

Suppose p[i] is the i-th prime, P[n]={p[i]| 1<=i<=n}. Since the only even prime is 2, the summary of P[n] is even iff n is odd. Conjecture: When n=2m+1 is odd, prime list P[n] can be partitioned into 2 non-overlapping sublists , each sublist has equal summary Total[P[n]]/2; When n=2m is even, prime list P[n] can be partitioned into 2 non-overlapping sublists , one sublist's summary is (Total[P[n]]-1)/2, the other's is (Total[P[n]]+1)/2. k = 2; Manipulate[P[n] = list = Prime[Range[1, n]]; Print[sum = Total[list]/k]; Select[Subsets[list, {(n - 1)/2}], Total[#] == sum &], {n, 3, 21, 2}] n=10, P[10]=Prime[Range[1, 10]] can be partitioned into equal 3 sublists. 43=129/3=3+11+29=7+13+23=2+ 5+17+ 19 Question: when prime list can be partitioned into equal 3 sublists? only if Total[P[n]]/3 is an integer? n = 20 FoldList[Plus, 0, Prime[Range[1, n]]] k = 3; n = 10; P[n] = list = Prime[Range[1, n]] sum = Total[list]/k Select[Subsets[list, {2, (n - 1)}], Total[#] == sum &] These codes is not good for solving this question. Can you help me?