To identify primitive paths, which are centerlines of confining tubes, two leading methods, namely total quadratic energy minimization and length minimization, are explored and compared in molecular dynamics (MD) simulations of linear pearl-necklace polymer chains. Energy minimization leads to a slightly larger averaged length but much narrower contour length distribution around the average length than does length minimization. Applications of both methods to melts of linear polymers in MD simulations confirm a quadratic entropic potential governing the primitive path length distribution. However, length minimization leads to a prefactor of around 1.5, in agreement with the classical result of Doi and Edwards, while energy minimization gives a prefactor of around 3.0.