For South America, for a long time it was Chimbote, in Chile, near Tupungato, but that was climbed last year. No idea what it is now.
The last of the 6000 meter peaks in the Atacama finally were climbed between 2000-2003. Undoubtedly, some (probably many) of the 5000 meter peaks are still left, not because of technical difficulty, but because of being isolated a very long way from any fresh water sources and being in the very desolate desert.
Outside the Atacama, it is possible that Cerro Campanario is still unclimbed (the northern one near Descabezado, not the one near Bariloche) , but it’s only 4000 meters.
Labuche Kang II
Do you mean Labuche Kang III? Labuche Kang II was (unless disputed?) climbed in 1995?
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I don't know what it would be in North America (certainly somewhere in Alaska-Canada), but in the Rocky Mountains the highest unclimbed peak
might be Red Castle (~12,700 feet/3870 meters). At least many sources claim that it has been unclimed (the actual Red Castle, not the non-technical mountain [12825] to the south which is sometimes referred to as Red Castle). Here is one:
http://utahikerguy.tumblr.com/I really don't know if it's true or not (in fact I'm somewhat skeptical), but in the last 20+ years I have heard from many people that it is still unclimed, or at least has no known ascents.
It actually doesn't
look that bad, but the rock is very bad:
So far all
known attempts failed because of loose rock. For example, I recently recieved this email from SP member Alpinglow84:
I was reading your High Uintas page and was wondering if anyone had sent
any information on climbing Red Castle. Two years ago my partner and I made
an attempt on a technical line on the West Face but were turned back after
two pitches because the rock is practically hardened mud and even good
looking holds (i.e. no fracture lines/well attached) would detach when
weighted. I got curious about what others may have said on the subject.
Thanks
Phil B.Red Castle has been attempted several times in recent years, but it seems that the story is the always the same and similar to the above. If anyone does know of any ascent of Red Castle, many would be interested in hearing about it.