Because the prime factor set N∋P_α={p_α∈P_α:2〖≤∀p〗_α,√n→∞} is a known set, and all composite numbers belong only to one of its minimum prime factor family sets N∋d_(σ≤α)⊂d_α.Prime factorization of integer with remainder division, solution of n^2 and higher order n^s indefinite equation, Legendre symbol (a/p_i ) Jacobi symbol (n/m), Euler function, etc