  A rare class of `super-luminous' supernovae that are about ten or more times
more luminous at their peaks than other types of luminous supernovae has
recently been found at low to intermediate redshifts. A small subset of these
events have luminosities that evolve slowly and result in radiated energies of
around 10^51 ergs or more. Therefore, they are likely examples of
`pair-instability' or `pulsational pair-instability' supernovae with estimated
progenitor masses of 100 - 250 times that of the Sun. These events are
exceedingly rare at low redshift, but are expected to be more common at high
redshift because the mass distribution of the earliest stars was probably
skewed to high values. Here we report the detection of two super-luminous
supernovae, at redshifts of 2.05 and 3.90, that have slowly evolving light
curves. We estimate the rate of events at redshifts of 2 and 4 to be
approximately ten times higher than the rate at low redshift. The extreme
luminosities of super-luminous supernovae extend the redshift limit for
supernova detection using present technology, previously 2.36, and provide a
way of investigating the deaths of the first generation of stars to form after
the Big Bang.
