Gangkhar Puensum In Bhutan is the important mountain. Gangkhar Puensum is the highest mountain in Bhutan and the highest unclimbed mountain in the world, with an elevation of 7,570 m and a prominence of over 2,990 m. 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.