Extremely large magnetoresistance and Shubnikov–de Haas quantum oscillation study of topological semimetal candidate <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>Pr</mml:mi> <mml:mi>X</mml:mi> </mml:math> <mml:math xmlns:mml="htt

Nonsaturated extremely large magnetoresistance (XMR), quantum oscillation (QO), and nontrivial Berry phase have been observed in many exotic quantum materials. But the underlying mechanisms driving these phenomena remain a puzzle. In this work, we present a comprehensive investigation of the structural, magnetic, XMR, and QO study of high-quality PrP, PrAs, and PrSb single crystals, alongside density functional theory $(\mathrm{DFT})+U$ calculations x-ray diffraction analyses indicate that the flux-grown high-quality PrX (where X represents P, As, or Sb) system exhibits a simple rock-salt type structure with R-3m symmetry (No. 225). Heat capacity and susceptibility measurements find that the 4f electrons of $\mathrm{P}{\mathrm{r}}^{3+}$ ions in all three compounds are localized and the PrX system shows a Van Vleck paramagnetic ground state without any structure transition. Quantum transport measurements reveal nearly quadratic behavior in the magnetoresistance and significant angular and temperature-dependent Shubnikov--de Haas oscillations, with small effective mass ${\mathrm{m}}_{0}$ of multiband charge carriers. Fast Fourier transformation analyses yield an electron pocket (\ensuremath{\alpha} band) located at the X point predominantly associated with the Pr d electrons, and two types of hole pockets (the outer \ensuremath{\beta} and inner \ensuremath{\gamma} pockets) at the \ensuremath{\Gamma} point, which primarily arise from the p orbitals of As or Sb. Comparison with $\mathrm{DFT}+U$ calculations indicate a crucial role of the 4f Coulomb interaction in influencing the topology of the band structures, particularly the presence of band crossing points. Our work provides a basis for in-depth investigations into the XMR, quantum oscillations, and Berry phase associated with band topology in lanthanum monopnictides and other innovative quantum material systems.