The core of this paper is to reveal the structural necessity that causes primes and new primes to form a symmetry, occurring from the cause-and-effect relationship between primes and composites. Regarding the boundary, if an arbitrary integer n is chosen, the set of consecutive numbers from 0 to n is defined as the 1st boundary and it extends using an arithmetic sequence with n elements but limits to n^2. After selecting n, therefore, n boundaries are generated from the 1st to nth, and each boundary contains n elements. Each prime wave in the 1st boundary connects to the composites that use the prime as a factor, and the remaining numbers between the 2nd and nth boundaries on the x-axis are all new primes in Series I. Under this condition, the primes in the 1st boundary and the new primes in the 2nd boundary form symmetry around the midpoint of even 2n caused by the asymmetry between primes and composites, Goldbach’s conjecture is satisfied in Series II and III. Therefore, Series IV explains the necessity for the primes and new primes to form a structural symmetry using 2 and 3, and discusses how this symmetry repeats at intervals of 30, generated by 5.