In this paper, we propose a novel pseudo chaotic random number generator based on three weakly-coupled discrete Skew tent maps. Its implementation was performed with C language and finite precision N=32, including a chaotic multiplexing technique. We show that our approach permits to avoid dynamic degradation caused by finite precision in one hand, and to allow emergence from chaos toward randomness in the other hand. As a consequence, the proposed generator turns out to be secure against famous cryptographic and statistical attacks. Several statistical tests such as correlation, histogram, chi2 and NIST have been applied on the generated sequences. They confirm the robustness of this chaotic generator.