The algebraic Atiyah-Hirzebruch spectral sequence of real projective spectra

In this note, we use Curtiss algorithm and the Lambda algebra to compute the algebraic Atiyah-Hirzebruch spectral sequence of the suspension spectrum of $mathbb{R}P^infty$ with the aid of a computer, which gives us its Adams $E_2$-page in the range of $t<72$. We also compute the transfer map on the Adams $E_2$-pages. These data are used in our computations of the stable homotopy groups of $mathbb{R}P^infty$ in [6] and of the stable homotopy groups of spheres in [7].