3D Gaussian Splatting (3DGS) has garnered significant attention due to its superior scene representation fidelity and real-time rendering performance, especially for dynamic 3D scene reconstruction (\textit{i.e.}, 4D reconstruction). However, despite achieving promising results, most existing algorithms overlook the substantial temporal and spatial redundancies inherent in dynamic scenes, leading to prohibitive memory consumption. To address this, we propose P-4DGS, a novel dynamic 3DGS representation for compact 4D scene modeling. Inspired by intra- and inter-frame prediction techniques commonly used in video compression, we first design a 3D anchor point-based spatial-temporal prediction module to fully exploit the spatial-temporal correlations across different 3D Gaussian primitives. Subsequently, we employ an adaptive quantization strategy combined with context-based entropy coding to further reduce the size of the 3D anchor points, thereby achieving enhanced compression efficiency. To evaluate the rate-distortion performance of our proposed P-4DGS in comparison with other dynamic 3DGS representations, we conduct extensive experiments on both synthetic and real-world datasets. Experimental results demonstrate that our approach achieves state-of-the-art reconstruction quality and the fastest rendering speed, with a remarkably low storage footprint (around \textbf{1MB} on average), achieving up to \textbf{40$\times$} and \textbf{90$\times$} compression on synthetic and real-world scenes, respectively.