What is the highest mountain in the world that has not yet been climbed?

Gangkhar Puensum in Bhutan-elevation 7570 metres(24,836 feet)

Gangkhar Puensum is the highest mountain in Bhutan and the highest unclimbed mountain in the world with an elevation of 7570 metres and a prominence of over 2990 metres. After Bhutan was opened for mountaineering in 1983 there were four expeditions that made failed summit attempts in 1985 and 1986. However, in 1998, a team from Tibet successfully climbed a subsidiary peak of the mountain.

Gangkhar Puensum, alternative transliteration Gangkar Punsum or Gankar Punzum, (meaning 3 mountain siblings"), had its altitude first measured in 1922, but maps of the region are not at all accurate and the mountain is shown in different locations and with markedly different heights. Indeed, because of inadequate mapping, the first team to attempt the summit was unable to find the mountain at all.

The book of the 1986 British expedition gives the mountain's height as 24,770 feet and states that Gangkhar Puensum is completely inside Bhutan whereas the nearby Kula Kangri is completely inside Tibet. Kula Kangri, 7554 metres, is a separate mountain 30 km to the northeast, which was first climbed in 1986. It is variously mapped and described as being in Tibet or Bhutan.

Since 1994, climbing of mountains in Bhutan higher than 6000 metres has been prohibited out of respect for local spiritual beliefs and since 2003, mountaineering has been forbidden completely. Gangkhar Puensum may keep its unique status for some time: any higher unclimbed peaks in the world are likely to be subsidiary tops, not separate mountains.

In 1998, a Japanese expedition secured permission from the Chinese Mountaineering Association to climb the mountain but permission was withdrawn because of a political issue with Bhutan. Instead, the team set off in 1999 from Tibet and successfully climbed the 7535 metre subsidiary peak, Liankang Kangri (also known as Gangkhar Puensum North). Unlike most maps, the expedition's report shows this summit as being in Tibet and the Tibet-Bhutan border is shown crossing the summit of Gangkhar Puensum, described as "the highest peak in Bhutan", at 7570 metres. This elevation is supported by Japanese sources which are in turn based on Chinese sources. It has not been surveyed by Bhutan.

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