  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(\frac{\alpha}{\pi}\right)^4$. I have fit a semi-analytical expression to
the numerical value. The expression contains harmonic polylogarithms of
argument $e^{\frac{i\pi}{3}}$, $e^{\frac{2i\pi}{3}}$, $e^{\frac{i\pi}{2}}$,
one-dimensional integrals of products of complete elliptic integrals and six
finite parts of master integrals, evaluated up to 4800 digits.
