Radio pulsars are rotating neutron stars that emit beams of radio waves fro
m regions above their magnetic poles. Popular theories(1-4) of the emission
mechanism require continuous electron-positron pair production with the po
tential responsible for accelerating the particles being inversely related
to the spin period. Pair production will stop when the potential drops belo
w a threshold, so the models predict that radio emission will cease when th
e period exceeds a value that depends on the magnetic field strength and co
nfiguration. Here we show that the pulsar J2144-3933, previously thought to
have a period of 2.84 s, actually has a period of 8.51 s, which is by far
the longest of any known radio pulsar, Moreover, under the usual model assu
mptions(5), based on the neutron-star equations of state, this slowly rotat
ing pulsar should not be emitting a radio beam. Therefore either the model
assumptions are wrong, or current theories of radio emission must be revise
d.