2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/144140In this paper a bijection between the set of prime ideals of a Leavitt path algebra $L_K(E)$ and a certain set which involves maximal tails in $E$ and the prime spectrum of $K[x,x^{-1}]$ is established. Necessary and sufficient conditions on the graph $E$ so that the Leavitt path algebra $L_K(E)$ is primitive are also found.Rings and Algebras16D70text