  Aims. The Crab nebula displayed a large gamma-ray flare on September 18,
2010. To more closely understand the origin of this phenomenon, we analyze the
INTEGRAL (20-500 keV) and FERMI (0.1-300 GeV) data collected almost
simultaneously during the flare. Methods. We divide the available data into
three different sets, corresponding to the pre-flare period, the flare, and the
subsequent quiescence. For each period, we perform timing and spectral analyses
to differentiate between the contributions of the pulsar and from the
surrounding nebula to the gamma-ray luminosity. Results. No significant
variations in the pulse profile and spectral characteristics are detected in
the hard X-ray domain. In contrast, we identify three separate enhancements in
the gamma-ray flux lasting for about 12 hours and separated by an interval of
about two days from each other. The spectral analysis shows that the flux
enhancement, confined below ~ 1 GeV, can be modelled by a power-law with a high
energy exponential cut-off, where either the cut-off energy or the model
normalization increased by a factor of ~ 5 relative to the pre-flare emission.
We also confirm that the gamma-ray flare is not pulsed. Conclusions. The timing
and spectral analysis indicate that the gamma-ray flare is due to synchrotron
emission from a very compact Pevatron located in the region of interaction
between the pulsar wind and the surrounding nebula. These are the highest
electron energies ever measured in a cosmic accelerator. The spectral
properties of the flare are interpreted in the framework of a relativistically
moving emitter and/or a harder emitting electron population.
