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Simulations of dislocation dynamics in single crystals of hcp zirconium are presented with emphasis on the hardening associated with prismatic slip at low temperature. Two original aspects of the simulation method are discussed, the treatment of the hcp lattice by an orthorhombic representation and the use of periodic boundary conditions. The mobility of screw and non-screw segments are defined in a phenomenological manner. Different investigations on the interactions between dislocations gliding in different prismatic planes show that no junction is formed between intersecting screw dislocations, which results in a rather small forest hardening at low temperature. This explains experimental observations of an initial deformation stage with a low strain hardening coefficient in zirconium or titanium crystals at low temperature.