We shall discuss three classes of numerical methods for Hamilton systems and three conjectures: Feng Kangs conjecture(i.e.,the deviation of computational orbits grows linearly with time: |z(tn)-Zn| ≤ C1tnh2m),quasi-symplecticity(i.e.,the deviation of symplecticity doesnt grow with time: |(DZn/DZo)TJ(DZn/DZo)-J|≤C2h2m),and quasi-preservation of energy(i.e.,the deviation of energy doesnt grow with time: |H(Zn)-H(Z(tn))|≤ C3h2m),where the constants Ci are independent of time tn.Numerical experiments exhibit several important facts as follows.Symplectic algorithms always preserve symplecticity,then Feng Kangs conjecture and quasi-conservation of energy hold.Continuous finite elements always are of conservation of energy,then Feng Kangs conjecture and quasi-symplecticity hold.Besides,if we define a broad class of regular algorithms which preserve Feng Kangs conjecture,we find that both quasi-symplecticity and quasi-conservation of energy still hold.Therefore,in the generalized sense,all these algorithms are equivalent or twin-brothers.