Why Everest's South Summit, taller than K2, isn't a mountain
Everest's South Summit stands higher than K2, the world's second-highest mountain, yet nobody counts it as a separate peak. The reason is prominence: how far you must descend from a summit before you can climb to anything taller. K2 rises more than four kilometres above its lowest link; the South Summit, barely eleven metres.
Prominence measures a summit's independence. Trace every route from a peak toward higher ground and note the lowest point on each; the highest of those low points is the key col, or saddle. Prominence is the peak's elevation minus that col's. A handy picture is to flood the land until the peak and its taller neighbour become separate islands, then drain it until a thin land bridge first joins them. That bridge is the key col. On any landmass, the highest peak's prominence simply equals its height.
Distances can be startling. Everest is the parent peak of Aconcagua in Argentina, 17,755 km away, and if sea level is ignored Aconcagua's key col is the Bering Strait. Mont Blanc's col lies by Lake Onega in Russia's northwest, just 113 m up, on the divide between Baltic and Caspian drainage, and its encirclement parent is again Everest. Because that definition lands far from intuition, Britain uses prominence parentage instead; otherwise almost any coastal hillock would have Ben Nevis as its parent. Under that scheme a chain climbs from Billinge Hill through Kinder Scout, Scafell Pike and Snowdon to Ben Nevis, with height and prominence rising at every step.
Mountaineers like the measure because it is objective yet tracks how important a summit feels: high-prominence peaks tend to be the local high point with commanding views. Lists of hills use it as a cutoff. The Nuttalls' list of English and Welsh mountains needs 15 m, Alan Dawson's Marilyns in Britain and Ireland need 150 m, and American fourteeners generally need 300 ft. In the US, 2000 ft has become an informal badge of major stature.
Ranking peaks by prominence alone, rather than by height, produces a very different list, dominated by isolated giants such as island high points and stratovolcanoes. Such a list needs no cutoff at all, since a highly prominent peak is automatically independent.
Source: Topographic prominence