In this paper, we study a structural condition on the ternary representations of odd integers, termed the Sum Cover Conjecture (SCC). For an odd integer p>69, let T(p) be the set of representations of p as a sum of three distinct prime numbers, and let P(p) denote the set of all primes that appear in at least one such representation. The Sum Cover Conjecture asserts that for every odd p>69, the set P(p) contains all odd primes q