In this research a theorem for primes to qualify for Goldbach partition composite even numbers is presented. In the paper reference [1] a neccessary and sufficient condition for proof of Goldbach partition of a composite number was es-tablished and proved. In the paper it was proved that the square of every integer greater than 1 is equal to the sum of the square of an integer greater or equal to zero and a Goldbach partitition semiprime. The proved theorem ef-fectively means that every composite even number has a composite even number. A Goldbach partition semiprime is a semiprime that is a product of two Goldbach partition primes. For a prime to be a Goldbach partition prime it hasto have a Goldbach partition partner for a the specific composite composite even number under consideration. In the paper reference [1] it was proved that every composite even number has at least 1 Goldbach partition semiprime for itsGoldbach parition. In this paper we shall closely examine the primes constituting the Goldbach partition semiprime.