因为素因子集(N∋P_α={p_α∈P_α:2〖≤∀p〗_α，√n→∞

Because the prime factor set (N∋P_α={p_α∈P_α:2〖≤∀p〗_α, √n→∞}) is a known set, all composite numbers belong to only one of its minimum prime factor family sets (N ∋d_(σ≤α)⊂d_α). Make prime factorization of integers with residual division, solve (n^2) and high-order (n^s) indefinite equations, Legendre symbol (a/p_i ), Jacobian symbol (n/m) can be used to distinguish the equation , and the Euler function etc. <br>are simplified or omitted together. The family sieve method (⇒) is carried out from small to large in the order of prime factors. Any composite number that has an overlapping relationship with the prime factor smaller than the current one is naturally filtered, so that the prime factor and composite number are reshaped into a simple and clear subordination relationship. It greatly simplifies the solution of composite number sets.

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 integers with remainder division, solution of (n ^ 2) and higher order (n ^ s) indefinite equations, Legendre symbol symbol (a/p_i), Jacobi symbol (n/m), and Euler function, etc<br>Simplify or omit both. The family screening method (⇒) is carried out in the order of prime factors from small to large, and any composite number that overlaps with the current prime factor is naturally filtered, reshaping the prime factor and composite number into a simple and clear subordinate relationship, greatly simplifying the solution of the composite number set.

Because the prime factor set (NP _ α = {p _ α ∈ p _ α: 2 [≤ p] _ α, √n→∞}) is a known set, all the composite numbers belong to only one of its smallest prime factor family sets (nd _ (σ≤ α) d _ α). Decomposition of prime factors of integers with division, solution of (n 2) and high-order (n s) indefinite equations, determination of solvability of Legendre symbols (a/p_i) and Jacobian symbols (n/m) to equations, and Euler function, etc.<br> Are simplified or omitted together. The family screening method () is carried out in the order of prime factors from small to large, and any composite number that overlaps with the current prime factor is naturally filtered, which reshapes the prime factor and composite number into a simple and clear subordinate relationship, greatly simplifying the solution of composite number set.