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Based on $10.4~\\rm{fb^{-1}}$ of $p \\overline p $ collision data collected by the D0 experiment at the Fermilab Tevatron collider, we report the first evidence for the prompt production of $X(4140)$ and find the fraction of $X(4140)$ events originating from $b$ hadrons to be $f_b=0.39\\pm 0.07 {\\rm \\thinspace (stat)} \\pm 0.10 {\\rm \\thinspace (syst)} $. 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