Since its discovery more than half a century ago Przybylski's star (HD101065) continues to excite the astronomical community by the unusual nature of its spectrum, exhibiting exotic element abundances. This star was also the first magnetic chemically peculiar A-type star for which the presence of rapid oscillations was established. Our analysis of newly acquired and historic longitudinal magnetic field measurements indicates that Przybylski's star is also unusual with respect to its extremely slow rotation. Adopting a dipolar structure for the magnetic field and using a sine wave fit to all reported longitudinal magnetic field values over the last 43yr, we find a probable rotation period P_rot ~ 188yr, which however has to be considered tentative as it does not represent a unique solution and has to be verified by future observations. Additionally, based on our own spectropolarimetric material obtained with HARPSpol, we discuss the impact of the anomalous structure of its atmosphere, in particular of the non-uniform horizontal and vertical distributions of chemical elements on the magnetic field measurements and the pulsational variability. Anomalies related to the vertical abundance stratification of Pr and Nd are for the first time used to establish the presence of a radial magnetic field gradient.

11 pages, 4 tables, 7 figures, accepted for publication in MNRAS