  We reexamine the general synchrotron model for GRBs' prompt emission and
determine the regime in the parameter phase space in which it is viable. We
characterize a typical GRB pulse in terms of its peak energy, peak flux and
duration and use the latest Fermi observations to constrain the high energy
part of the spectrum. We solve for the intrinsic parameters at the emission
region and find the possible parameter phase space for synchrotron emission.
Our approach is general and it does not depend on a specific energy dissipation
mechanism. Reasonable synchrotron solutions are found with energy ratios of
$10^{-4}<\epsilon_B/\epsilon_e<10$, bulk Lorentz factor values of
$300<\Gamma<3000$, typical electrons' Lorentz factor values of $3\times
10^3<\gamma_e<10^5$ and emission radii of the order $10^{15}cm<R<10^{17}$cm.
Most remarkable among those are the rather large values of the emission radius
and the electron's Lorentz factor. We find that soft (with peak energy less
than 100KeV) but luminous (isotropic luminosity of $~1.5 \times 10^{53}$)
pulses are inefficient. This may explain the lack of strong soft bursts. In
cases when most of the energy is carried out by the kinetic energy of the flow,
such as in the internal shocks, the synchrotron solution requires that only a
small fraction of the electrons are accelerated to relativistic velocities by
the shocks. We show that future observations of very high energy photons from
GRBs by CTA, could possibly determine all parameters of the synchrotron model
or rule it out altogether.
