We present a flare catalog of the Kepler mission using the long-cadence data of Data Release 25. This catalog comprises 3420 flare stars and 162262 flare events. A comparison shows that the flare catalogs of previous studies are seriously polluted by various false-positive signals and artifacts. The incidence of flare stars rises with decreasing temperature, which accords with the theoretical analysis. The flare frequency distributions (FFDs) from F-type stars to M-type stars obey a power-law relation with {alpha}~2, indicating that they have the same mechanism on generating flares. The remarkable incidence and the deviation of FFDs on A-type flare stars imply that they generate flares in a different way. The activity-rotation relation is consistent with previous studies at low temperature bands, whereas it becomes dispersive with increasing temperature. Combined with the Gyrochronology, we find that the mixing of stars of two different dynamos gives rise to the dispersion. We thereby propose a scenario on understanding the activity-rotation relation across the Hertzsprung-Russell diagram. Based on the scenario and the correspondence of dynamo with regard to activity and rotation, we suggest a new expression on the activity-rotation relation, in which the segmentation is on the basis of the dynamo rather than the rotation period. The rotation distribution of flare stars shows that about 70% of flare stars rotate faster than 10 days and the rate approaches 95% at 30 days. Based on the incidence and the rotation distribution of flare stars, we estimate that a superflare with energy ~10^34^erg occurs on the Sun at least once in 5500yr.

Cone search capability for table J/ApJS/241/29/table1 (Parameters of flaring stars -- from erratum published in 2020, ApJS, 250, 25)