TITLE:
Decomposing Even Integers into Prime and Composite Parts
AUTHORS:
Seonghwan Yang
KEYWORDS:
Even Integers, Prime Number, Composite Number, Number Theory, Decomposition
JOURNAL NAME:
Open Journal of Discrete Mathematics,
Vol.15 No.4,
September
3,
2025
ABSTRACT: Let
n≥10
be an even integer. It is proved that there exists a prime number
p
and a composite number
c
such that
n=p+c
. The proof is constructed using elementary number theory, incorporating inductive reasoning, deterministic candidate filtering, and contradiction-based exclusion. This result provides a structural decomposition of even integers as prime-Composite sums, without reliance on probabilistic or analytic methods.