This is a list of mountain peaks ordered by their topographic prominence.
The prominence of a peak is the minimum height of climb to the summit on any route from a higher peak, or from sea level if there is no higher peak. The lowest point on that route is the col.
For full definitions and explanations of topographic prominence, key col, and parent, see topographic prominence. In particular, the different definitions of the parent of a peak are addressed at length in that article. Height on the other hand simply means elevation of the summit above sea level.
Regarding parents, the prominence parent of peak A can be found by dividing the island or region in question into territories, by tracing the runoff from the key col (mountain pass) of every peak that is more prominent than peak A. The parent is the peak whose territory peak A resides in.
The encirclement parent is found by tracing the contour below peak A's key col and picking the highest mountain in that region. This is easier to determine than the prominence parent; however, it tends to give non-intuitive results for peaks with very low cols such as Jabal Shams which is #110 in the list.
Either sort of parent of a typical very high-prominence peak such as Denali will lie far away from the peak itself, reflecting the independence of the peak.
Most sources (and the table below) define no parent for island and landmass highpoints; others treat Mount Everest as the parent of every such peak with the world ocean as the "key col".
The following table lists the Earth's 125 most topographically prominent summits. Of these, Indonesia has the most, with 13. Close behind it are China and the United States with 12.
The list of peaks that follows is not complete, but the peaks are all notable. Island high points (whose prominence is equal to their elevation) can be found at the List of islands by highest point; hence most are not included below. Some well-known peaks listed here do not score highly by prominence.
All peaks with a prominence of more than 1,500 metres rank as an Ultra. For a complete listing of all 1,524 peaks with prominence greater than this level, see the lists of Ultras.
In the table, the prominence parent is marked "1", and the encirclement parent "2". Where a single parent is listed, the different definitions agree.
*.^ By convention, cols created by human activity are not counted. Therefore, the Suez, Panama and other canals are ignored in these calculations. Cuts that lower the natural elevations of mountain passes are also ignored.[16] Towers, monuments and similar on the peaks are also ignored.
