We utilized the all-copropagating scheme, which maintains the phase-match condition, in the spontaneous four-wave mixing (SFWM) process to generate biphotons from a hot atomic vapor.The scheme enables our biphotons not only to surpass those in the previous works of hot-atom SFWM, but also to compete with the biphotons that are generated by either the cold-atom SFWM or the cavity-assisted spontaneous parametric down conversion. The biphoton linewidth in this work is tunable for an order of magnitude. As we tuned the linewidth to 610 kHz, the maximum twophoton correlation function, gs,as , of the biphotons is 42. This gs,as violates the Cauchy-Schwartz inequality for classical light by 440 folds, and demonstrates that the biphotons have a high purity.The generation rate per linewidth of the 610-kHz biphoton source is 1,500 pairs/(s•MHz), which is the best result of all the sub-MHz biphoton sources in the literature. By increasing the pump power by 16 folds, we further enhanced the generation rate per linewidth to 2.3×10 4 pairs/(s•MHz), while the maximum g (2) s,as became 6.7. In addition, we are able to tune the linewidth down to 290±20 kHz. This is the narrowest linewidth to date, among all the various kinds of single-mode biphotons.