Scatter plot of the E  >  10 MeV peak proton flux vs. the X-ray flare intensity of our new sample (blue dots). The solid black line corresponds to the RMA regression fit of our sample corresponding to with β = 1.40 ± 0.19. The red dashed line gives the upper solar limit from Takahashi et al. (2016) based on a scaling law of . In the figure, this relation was re-scaled to the upper-point in our sample presented as a red dot, suggesting a new upper limit that is slightly below the previously reported limit by Takahashi et al. (2016).