  Single photon detection played an important role in the development of
quantum optics. Its implementation in the microwave domain is challenging
because the photon energy is 5 orders of magnitude smaller. In recent years,
significant progress has been made in developing single microwave photon
detectors (SMPDs) based on superconducting quantum bits or bolometers. In this
paper we present a practical SMPD based on the irreversible transfer of an
incoming photon to the excited state of a transmon qubit by a four-wave mixing
process. This device achieves a detection efficiency $\eta = 0.43$ and an
operational dark count rate $\alpha = 85$ $\mathrm{s^{-1}}$, mainly due to the
out-of-equilibrium microwave photons in the input line. The corresponding power
sensitivity is $\mathcal{S} = 10^{-22}$ $\mathrm{W/\sqrt{Hz}}$, one order of
magnitude lower than the state of the art. The detector operates continuously
over hour timescales with a duty cycle $\eta_\mathrm{D}=0.84$, and offers
frequency tunability of at least 50 MHz around 7 GHz.
