  Formal analyses of blockchain protocols have received much attention
recently. Consistency results of Nakamoto's blockchain protocol are often
expressed in a quantity $c$, which denotes the expected number of network
delays before some block is mined. With $\mu$ (resp., $\nu$) denoting the
fraction of computational power controlled by benign miners (resp., the
adversary), where $\mu + \nu = 1$, we prove for the first time that to ensure
the consistency property of Nakamoto's blockchain protocol in an asynchronous
network, it suffices to have $c$ to be just slightly greater than
$\frac{2\mu}{\ln (\mu/\nu)}$. Such a result is both neater and stronger than
existing ones. In the proof, we formulate novel Markov chains which
characterize the numbers of mined blocks in different rounds.
