pulsars that had been observed to produce giant pulses out of more than 1500 known pulsars. The giant pulses of PSR B1937+21 were first observed in 1984, shortly after its discovery, but difficulty in observing single pulses of PSR B1937+21 due to its fast period meant that the pulses were not studied in more depth until a decade after they were first observed. In more recent follow up observations, more giant pulses have been found. These giant pulses have been observed to occur at the trailing edge of both the pulse and interpulse. The duration of these giant pulses is short compared to the period of the pulsar, lasting on the order of 10 nanoseconds. The flux density of observed pulses is somewhat variable, but has been observed to be as high as 6.5 W m−2Hz−1 (6.5 janskys). The brightness temperature of a pulse with such high flux density and such low duration exceeds 5 kelvins, making the pulses of PSR B1937+21 the brightest radio emission ever observed. PSR B1937+21 is intrinsically the most luminous millisecond pulsar. In addition to the radio pulses observed, pulses have been detected at x-ray wavelengths, which show the same pulse and interpulse pattern. Evidence for companions After the discovery of planetary mass companions around PSR B1257+12 in 1990 by Aleksander Wolszczan, data for PSR B1937+21 and other pulsars were analyzed for the presence of similar companions. By 1994, an upper limit of about one thousandth of the mass of Earth was determined for any companion of PSR B1937+21 within 2 astronomical units. In 1999, Aleksander Wolszczan reported variations in the times of arrival of pulses from PSR B1937+21, as well as previous analysis by Tokio Fukushima which suggested that these timing variations could be caused by a dwarf planet around the pulsar. The data were consistent with a companion having a mass similar to Ceres and located at 2.71 astronomical units from the pulsar, but data over a longer period of time are required in order to verify the proposed companion. More recent observations have not detected any regular periodic signal associated with this companion, but argue that the slight variations in pulse arrival times are consistent with an asteroid belt having a total mass less than 0.05 that of the Earth, but acknowledge that the detection of periodicity in pulse timing variations associated with individual asteroids is necessary to confirm the possible asteroid