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Three direct semiconductor materials and one indirect semiconductor material, <i>Pm</i>&#8722;3<i>n</i> XN (X = B, Al, Ga, In), are investigated in our work, employing density functional theory (DFT), where the structural properties, stability, elastic properties, elastic anisotropy properties and electronic properties are included. The shear modulus <i>G</i> and bulk modulus <i>B</i> of <i>Pm</i>&#8722;3<i>n</i> BN are 290 GPa and 244 GPa, respectively, which are slightly less than the values of <i>B</i> and <i>G</i> for c-BN and <i>Pnma</i> BN, while they are larger than those of C₆₄ in the <i>I</i>4₁/<i>amd</i> phase. The shear modulus of <i>Pm</i>&#8722;3<i>n</i> BN is the greatest, and the shear modulus of C₆₄ in the <i>I</i>4₁/<i>amd</i> phase is the smallest. The Debye temperatures of BN, AlN, GaN and InN are 1571, 793, 515 and 242 K, respectively, using the elastic modulus formula. AlN has the largest anisotropy in the Young&#8217;s modulus, shear modulus, and Poisson&#8216;s ratio; BN has the smallest elastic anisotropy in <i>G</i>; and InN has the smallest elastic anisotropy in the Poisson&#8217;s ratio. <i>Pm</i>&#8722;3<i>n</i> BN, AlN, GaN and InN have the smallest elastic anisotropy along the (111) direction, and the elastic anisotropy of the <i>E</i> in the (100) (010) (001) planes and in the (011) (101) (110) planes is the same. The shear modulus and Poisson&#8217;s ratio of BN, AlN, GaN and InN in the <i>Pm</i>&#8722;3<i>n</i> phase in the (001), (010), (100), (111), (101), (110), and (011) planes are the same. In addition, AlN, GaN and InN all have direct band-gaps and can be used as a semiconductor within the HSE06 hybrid functional.