  For $\frac{1}{2}<x<1$, $y>0$ and $n\in\mathbb{N}$, let
$\displaystyle\theta_n(x+iy)=\sum_{i=1}^n\frac{{\mbox{sgn}}\,
q_i}{q_i^{x+iy}}$, where $Q=\{q_1,q_2,q_3,\cdots\}$ is the set of finite
product of distinct odd primes and ${\mbox{sgn}}\, q=(-1)^k$ if $q$ is the
product of $k$ distinct primes. In this paper we prove that there exists an
ordering on $Q$ such that $\theta_n(x+iy)$ has a convergent subsequence. As an
application, we prove the Riemann hypothesis.
