This article discusses our statistical investigations into the occurrence of proton events for solar energetic particle (SEP) alerts in space weather forecasts. We analyzed X-ray flux and proton intensity data obtained with the GOES satellite in the 23rd solar cycle. We found that the total soft X-ray flux (1--8¿) of almost all flares related to proton events exceeded a threshold value, which was ~20 ergs cm-2. This means that there is a threshold in flare duration in regard to peak X-ray flux and this is ~30 min for an M1.0 flare and/or 3 min for an X1.0 flare. We also confirmed this threshold with data in the 22nd solar cycle. These results will provide some of the most important criteria for SEP alerts and solar proton event forecasts in the future.