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We present four new fast radio bursts discovered in a search of the Parkes 70-cm pulsar survey data archive for dispersed single pulses and bursts. We searched dispersion measures (DMs) ranging between 0 and 5000 pc cm−3 with the HEIMDALL and FETCH detection and classification algorithms. All four of the fast radio bursts (FRBs) discovered have significantly larger widths (>50 ms) than almost all of the FRBs detected and catalogued to date. The large pulse widths are not dominated by interstellar scattering or dispersive smearing within channels. One of the FRBs has a DM of 3338 pc cm3, the largest measured for any FRB to date. These are also the first FRBs detected by any radio telescope so far, predating the Lorimer Burst by almost a decade. Our results suggest that pulsar survey archives remain important sources of previously undetected FRBs and that searches for FRBs on time-scales extending beyond ∼100 ms may reveal the presence of a larger population of wide-pulse FRBs.