4. On a distant island, there live vegetarians who always tell the truth, and cannibals who always lie. One day, a vegetarian and several other islanders lined up, and each one said: "All vegetarians stand from me at a prime number of people apart." How many islanders could have lined up?
Answer: Any quantity.

Solution: Consider the following arrangement of the island's inhabitants (vegetarians are denoted by the letter "V", cannibals by the letter "C"): $V C C V C C V C \underbrace{C \ldots C}_{\text{any quantity}}$. Each vegetarian stands either 2 or 5 positions away from another vegetarian, so the statement is true for them. For cannibals who stand next to or one position away from any vegetarian, the statement is false (recall that 1 is not a prime number!). For cannibals standing in the right part, either the 1st or the 2nd vegetarian stands an even number of positions away (greater than 2), so the statement is also false for them. Thus, a row can be formed with 6 or more island inhabitants.

It is directly verified that $1,2,3,4,5$ inhabitants can also be arranged so that the condition of the problem is satisfied. For example, take the initial segments of the proposed arrangement.