The third Zemach moment and the size of the proton

To resolve the puzzle of the proton size raised from the recent result of muonic hydrogen Lamb shift, De R\'{u}jula has proposed that a large value of the third Zemach moment $< r^3_{p}>{(2)}$ of the proton to be the solution. His suggestion has been criticized by many groups based on the $ep$ scattering data at low $Q^2$ regime. However, if there is a "thorn" or "lump" in the electric form factor of the proton $G_{E}(Q^2)$ at extremely low $Q^2$ regime, then the third Zemach moment $< r^3_{p}>{(2)}$ would be as large as De R\'{u}jula suggested. In this article, we show that the existence of such a "thorn" or "lump" has not been completely excluded, although tightly restricted, by the current data of $ep$ elastic scattering. We also suggest a more sophisticated global fitting procedure of $G_{E}(Q^2)$ for the future fitting.