  The magnetic hyperfine structure constants have been calculated for low-lying
levels in neutral potassium atom taking into account the Bohr--Weisskopf (BW)
and Breit--Rosenthal (BR) effects. According to our results the $4p_{1/2}$
state of K~I is free from both BR and BW corrections on the level of the
current theoretical uncertainties. Using this finding and the measured values
of the $A(4p_{1/2})$ constants, we corrected the nuclear magnetic moments for
several short-lived potassium isotopes. The BW correction is represented as a
product of atomic and nuclear factors. We calculated the atomic factor for the
ground state of K I, which allowed us to extract nuclear factors for potassium
$I^\pi = 3/2^+$ isotopes from the experimental data. In this way the
application range of the single-particle nuclear model for nuclear-factor
calculation in these isotopes has been clarified.
