The product m_p*c is also the denominator in the formula of the proton Compton wavelength: W_C = h/(m_p*c), where h is the Planck constant.
It appears that m_p*c is also the main constant in the formula of the relativistic momentum of the proton, if such formula is written as the product of a dimensionless factor and a constant with the same dimensions as the relativistic momentum. For instance, here we write p = [1/(c^2/v^2 - 1)^(1/2)]*m_p*c instead of the standard formula p = [1/(1 - v^2/c^2)^(1/2)]*m_p*v, where v is the speed of the proton. A trigonometric version of the formula is p = tan(x)*m_p*c hence tan(x) = p/(m_p*c) assuming that sin(x) = v/c and 0 < x < Pi/2. Also p = sinh(X)*m_p*c assumnig that sin(x) = tanh(X) = v/c.
Also m_p*c is the main constant in the formula of the relativistic momentum of the proton, if such formula is written as p = [(E^2/E_0^2 - 1)^(1/2)]*m_p*c where E is the relativistic energy and E_0 is the energy at rest.
Also m_p*c is equivalent to the momentum of a photon whose energy is the same as the rest energy of a proton.
Also m_p*c is equivalent to the relativistic momentum of a proton whose velocity is equal to c/sqrt(2). For more information see A229962.