  We report the first statistical detection of X-ray emission from cosmic web
filaments in ROSAT data. We selected 15,165 filaments at 0.2<z<0.6 ranging from
30 Mpc to 100 Mpc in length, identified in the Sloan Digital Sky Survey (SDSS)
survey. We stacked the X-ray count-rate maps from ROSAT around the filaments,
excluding resolved galaxy groups and clusters above the mass of ~3 * 10^13 Msun
as well as the detected X-ray point sources from the ROSAT, Chandra, and
XMM-Newton observations. The stacked signal results in the detection of the
X-ray emission from the cosmic filaments at a significance of 4.2 sigma in the
energy band of 0.56-1.21 keV. The signal is interpreted, assuming the
Astrophysical Plasma Emission Code (APEC) model, as an emission from the hot
gas in the filament-core regions with an average gas temperature of
0.9(+1.0-0.6) keV and a gas overdensity of ~30 at the center of the filaments.
Furthermore, we show that stacking the SRG/eROSITA data for ~2,000 filaments
only would lead to a ~5 sigma detection of their X-ray signal, even with an
average gas temperature as low as ~0.3 keV.
