I have evaluated up to 1100 digits of precision the contribution of the 891 4-loop Feynman diagrams contributing to the electron $g$-$2$ in QED. The total mass-independent 4-loop contribution is $ a_e = -1.912245764926445574152647167439830054060873390658725345{\ldots} \left(\fracαπ\right)^4$. I have fit a semi-analytical expression to the numerical value. The expression contains harmonic polylogarithms of argument $e^{\frac{iπ}{3}}$, $e^{\frac{2iπ}{3}}$, $e^{\frac{iπ}{2}}$, one-dimensional integrals of products of complete elliptic integrals and six finite parts of master integrals, evaluated up to 4800 digits.

14 pages, 3 figures, 3 tables v2: version published in PRL (specified "mass-independent contribution", figure 2 reformatted)