回复：印尼奥赛题：素数（2星）

for 5, it is impossible, prove by contradiction. Suppose such 5 numbers exist:
(1) Non of the 5 numbers can be even, otherwise, it is always possible to pick 3 numbers whose sum is even.
(2) Consider the remainders of the 5 numbers mod 6, since non of the numbers is even, the remainders can only be 1,3 or 5. We have
(2.1) 1,3,5 can not all appear in the set of remainders, otherwise, 1+3+5 = 9 divides 3
(2.2) Because of (2.1), one of 1,3,5 should appear at least 3 times, but by adding 3 numbers who has the same remainders (mod 6) also leads to a sum which divides 3. Contradiction.