We present a search for binary neutron star mergers that produced gravitational-waves during the first observing run of Advanced LIGO and gamma-ray emission seen by either -BAT or Fermi-GBM, similar to GW170817 and GRB 170817A. We introduce a new method using a combined ranking statistic to detect sources that do not produce significant gravitational-wave or gamma-ray burst candidates individually. The current version of this search can increase by 70% the detections of joint gravitational-wave and gamma-ray signals. We find one possible candidate observed by LIGO and Fermi-GBM, 1-OGC 151030, at a false alarm rate of 1 in 13 years. If astrophysical, this candidate would correspond to a merger at Mpc with source-frame chirp mass of . If we assume the viewing angle must be to be observed by -GBM, our estimate of the distance would become Mpc. By comparing the rate of binary neutron star mergers to our search-estimated rate of false alarms, we estimate that there is a 1 in 4 chance this candidate is astrophysical in origin.

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