Natural X-rays from across the space are of very high energy but luckily our atmosphere shields us. This means X-ray telescopes must be above the atmosphere to see distant objects emitting X-rays.
More than 100,000 X-ray sources have been detected across the Universe. The most distant object seen in X-rays is 13 billion lightyears from Earth
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http://www.zietmysore.org/stud_mats/XII/PHYSICS/em%20wave-hots.pdf