I don't know that Messner climbed Everest twice in one week but... he and Peter Habeler were the first to ascend Everest without supplemental oxygen back in the 70s. He also summited all fourteen 8,000 meter peaks in the world without oxygen (1st to do so) and did them all in cat-quick "alpine style" including a solo ascent of K2 while his girlfriend and a buddy kept base camp for 3-4 days. Messner was and still is the **** of mountaineering.
What makes K2 (aka "Mount Godwin-Austen") so difficult is the 110-mile hike out from the last road to the base of the mountain. That, in itself, is an adventure for most people. Furthermore, the porters for hire (Baltis) have nowhere near the skills, dedication and work-ethic of the Sherpas of Everest lore. Jim Whittaker (1st American on Everest in '63) led a massive K2 expedition in '75 that failed miserably due to Balti strikes and internal strife. I believe they topped out at 21,000 feet - well short of the 28,000+ summit of K2. Photography Galen Rowell (Note: Mac guy) wrote a book called "In The Throne Room of The Mountain Gods" which details this expedition and previous ones.
Probably the most famous name to attempt K2 was Aleister Crowley - the 666 dude.
Sorry for the soapbox and the longwindedness.