  High harmonic generation traditionally combines ~100 near-infrared laser
photons, to generate bright, phase matched, extreme ultraviolet beams when the
emission from many atoms adds constructively. Here we show that by guiding a
mid-infrared femtosecond laser in a high pressure gas, ultrahigh harmonics can
be generated up to orders > 5000, that emerge as a bright supercontinuum that
spans the entire electromagnetic spectrum from the ultraviolet to > 1.6 keV,
allowing in-principle the generation of pulses as short as 2.5 attoseconds. The
multi-atmosphere gas pressures required for bright, phase matched emission also
supports laser beam self-confinement, further enhancing the x-ray yield.
Finally, the x-ray beam exhibits high spatial coherence, even though at high
gas density, the recolliding electrons responsible for high harmonic generation
encounter other atoms during the emission process.
