In her paper, "The Theory of Integer Multiplication with Order Restricted to Primes is Decidable" Françoise Maurin claims the following
On the other hand, J. Robinson shows in [12] that the theory of the integer multiplication with usual order < is not decidable.
The citation is to Robinson's paper "Definability and decision problems in arithmetic".
From which facts of [12] does the undecidability result follow?
Theorem 1.1 of Robinson's paper says that $+$ is definable in the structure $(\mathbb{N},\times,<)$. It follows by Gödel's Theorem that the complete theory of this structure is undecidable.
See Section 4 (pp. 110-113) for more on undecidability.