Minimum γ-ray flux in the hadronic scenario obtained assuming that the Perseus radio mini-halo has a secondary origin and that ϵ_B ≫ ϵ_CMB + ϵ_SD. We show the EBL-corrected fluxes for different spectral indexes α, adopting as reference the total synchrotron luminosity measured both at 327 MHz (Gitti et al. 2002) and at 1.4 GHz (Pedlar et al. 1990). We compare these with our 95%-c.l. point-like upper limits appropriately scaled for the radio surface brightness shape, i.e., multiplied by a factor of 1.15 with respect to what is reported in Table 2. The flux is integrated up to 10 TeV.