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  The 2013 champion said he played "one of the best rounds of his life" but "felt like crying" after missing a 15-foot birdie putt on the 18th for a 62.
  Compatriot Patrick Reed and Germany's Martin Kaymer are second on five under.
  England's Andy Sullivan is four under, one ahead of compatriot Justin Rose, while Rory McIlroy carded a 69.
  Mickelson made the most of glorious conditions on the west coast of Scotland, covering the front nine in 32 and the usually more treacherous back nine in 31. The 46-year-old made eight birdies and did not drop a shot.
  Phil, you made a beautiful read and putt on that last hole, but got absolutely stone-cold robbed.
  Nine players had carded 63s in 144 previous Opens, the last being McIlroy at St Andrews in 2010. But Mickelson's round was the lowest in an Open at Troon.
  "It was a fun round," he told BBC Sport. "Yet I still walk away wanting to shed a tear with that putt lipping out.
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  "I had a chance to do something historical. With a foot to go I thought it was in - I am not sure how it missed. The heartbreak of that is overshadowing my round right now."
  Reed made an eagle and five birdies in his five-under-par round, while 2014 Open champion McIlroy was four under at the turn but double-bogeyed the 13th.
  World number one Jason Day failed to capitalise on the more forgiving front nine and after eight pars on the homeward nine bogeyed the last to finish two over.
  Pre-tournament favourite and reigning US Open champion Dustin Johnson started with a 71, the same as two-time major winner and world number three Jordan Spieth, while fellow American and world number five Bubba Watson was five under after six holes before a triple-bogey at the notorious par-three eighth saw him post a one-under 70.
  Defending champion Zach Johnson was six under after 16 holes but bogeys on the final two holes saw him join five fellow Americans on four under.
  Justin Thomas,Steve Stricker, Billy Horschel, Tony Finau and Keegan Bradley also all shot 67s, while compatriot Rickie Fowler carded a 69.
  Players from the United States have won the last six Opens staged at Royal Troon.
  Wales' Jamie Donaldson, who has endured a poor season after an incident with a chainsaw damaged his left hand in January, carded a 69.
  South Africa's Louis Oosthuizen, winner of the Claret Jug in 2010, made a hole-in-one at the 14th in his round of 71, the same as England's reigning Masters champion Danny Willett.
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  McIlroy said he was happy with his "solid" start and that he expects scoring to become far more difficult if conditions deteriorate, as they are expected to do on Friday.
  "Today was a day where you had to make the most of conditions because I don't think we're going to see the course like this for the rest of the week," said the 27-year-old, who missed last year's Open at St Andrews because of injury.
  "I'm hoping some of the weather forecasts I've seen are right and that it's starting to clear up a little in the afternoon. But it's the Open Championship and you know coming here you're going to have to battle the elements somewhat."
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  World number 13 Reed tuned up for Troon with an appearance at the Scottish Open, where he finished tied for 10th in awful weather conditions.
  "It was cold, windy, rainy and I didn't see the sun once in Inverness," said the 25-year-old, who is playing in his third Open.
  "Today was a lot easier than I had to deal with last week and it allowed me to be a little bit more aggressive with my irons into the greens.
  "It's one of those golf courses that allows you to get off to a good start, so that you can get cocky and too careless on the back nine. You have to stay humble."
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  2013 US Open champion Rose, 35, said it was the best he had played for some time, having struggled with a back injury this season.
  "The score didn't really reflect how well I played," said Rose, whose top-10 finish last year was his best showing at The Open since tying for fourth as an amateur at Royal Birkdale in 1998.
  "Typical me, playing the back nine in fewer shots than the front nine. But I'm certainly happy with the start."
  The nature of Troon's Old Course was better demonstrated by South African Haydn Porteous, who went out in 30, including two eagles, and came home in 40.
  Day, who missed last year's play-off at St Andrews by one shot before winning the PGA Championship, his first major title, admitted he was struggling with his swing.
  "Every time I hit an iron I kept missing everything left and it caught me off guard," said the 28-year-old Australian.
  "It's frustrating but the next few days are going to be very difficult and if I can just play good, solid golf I can inch my way back in."
  Spieth, who also missed last year's play-off by one shot, was at a loss to explain his poor putting, which is usually his strongest suit.
  "My [putting] stroke's been great heading into here," said the 22-year-old, who had 33 putts in his first round, nine more than Reed.
  "I was much improved tee to green, struck the ball tremendously well, it just seemed like it didn't want to go in the hole once I got on the greens."
  Colin Montgomerie, an honorary member of Royal Troon, was first to tee off at 06:35 BST and double-bogeyed the opening hole.
  However, the 53-year-old Scot, who came through qualifying, reeled off five birdies to turn in 33 before three bogeys on the back nine gave him a level-par 71.
  "You'll see three- and four-under on the way out and then it's a matter of hanging on on the way back," said Montgomerie, a five-time major runner-up.
  "And remember, this course hasn't shown its teeth at all. Today was three out of 10. On Friday we're talking seven or eight out of 10, and then it's going to be very different."
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target: America's Phil Mickelson carded a 63, the joint-lowest round in major history, to lead on eight under after day one of The Open at Royal Troon.