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Assuming the obvious definitions below, we show that a decidable model that is effectively prime is also effectively atomic. This implies that two effectively prime (decidable) models are computably isomorphic. This is in contrast to the theorem that there are two atomic decidable models which are not computably isomorphic. We end with a section describing the implications of this result in reverse mathematics.Proof. Use a back-and-forth construction with complete formulas determining how to extend the partial isomorphism. Theorem 2. (Atomic ⇒ Prime) If A is a countable atomic model of T , then A is prime.Proof. Use the "forth" half of the back-and-forth argument. Theorem 3. (Prime ⇒ Atomic) IfA is a prime model of T , then A is countable and atomic.Proof. By the compact theorem T has a countable model. Therefore A is countable. Let a ∈ A , and consider its type. For any other model B of T , there is an elementary embedding of A into B, so that B also realizes this type. By the Omitting Types Theorem, the type of a includes a complete formula.