A memory device, a method for programming the memory device, a program verification method, and a memory system are provided. In the program verification method, an ith verification result of an ith program verification operation is obtained, where programming states verified by the ith program verification operation range from an nth state to an (n+k)th state, i and n are positive integers, k is a natural number, and the (n+k)th state is less than or equal to a highest programming state of the memory device; a range of programming states to be verified by an (i+1)th program verification operation is determined according to a verification sub-result for the nth state and a verification sub-result for the (n+k)th state in the ith verification result; and the (i+1)th program verification operation is executed according to the determined range of the programming states to be verified by the (i+1)th program verification operation.