  In this note, we use Curtis's 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].
