Already mentioned in the overview that Hayford is one of the 57 prominence peaks, I'd like to add just a bit more on the subject:
Hayford Peak comes in at #7 on this list of Nevada prominence peaks. While it is not one of the highest peaks in Nevada, it stands out rather dramatically from valleys around it, giving it 5392 feet of prominence. This prominence puts it in an elite group of peaks (already pointed out) in the USA that have a prominence of over 5000 feet and those can be seen on this neat MAP HERE. If you don't understand what prominence is all about, here is a good explanation. Adam Helman recently authored a book completely dedicated to prominence.