  We study the randomized rumor spreading algorithm \emph{pull} on complete
graphs with $n$ vertices. Starting with one informed vertex and proceeding in
rounds, each vertex yet uninformed connects to a neighbor chosen uniformly at
random and receives the information, if the vertex it connected to is informed.
The goal is to study the number of rounds needed to spread the information to
everybody, also known as the \emph{runtime}.
  In our main result we provide a description, as $n$ gets large, for the
distribution of the runtime that involves a martingale limit. %We provide a
description of the distribution of the runtime in terms of a limit of a
sequence of martingales. This allows us to establish that in general there is
no limiting distribution and that convergence occurs only on suitably chosen
subsequences $(n_i)_{i \in \mathbb{N}}$ of $\mathbb{N}$, namely when the
fractional part of $(\log_2 n_i +\log_2\ln n_i)_{i \in \mathbb{N}}$ converges.
