GULLANE, Scotland — Byeong Hun An played well enough in the Scottish Open on Thursday that he had reason to hope he can stick around for more links golf next week.

An ran off four straight birdies early in his round at The Renaissance Club and closed with a 25-foot birdie putt on the tough par-3 ninth hole for a 9-under 61, giving him a two-shot lead over Davis Riley.

An had his best score on the PGA Tour — the Genesis Scottish Open is co-sanctioned with the European tour — and it came at just the right time. This is the final tournament for players to try to earn a spot in The Open next week at Royal Liverpool. The leading three players not already exempt will earn spots.

“It’s one of those days, every shot you hit just has a perfect number,” An said. “Pitched right, how the ball reacted on the greens, everything was perfect. Some of the putts I had were very straightforward putts that I think I left in a good spot. Everything went really well.”

Rory McIlroy had few complaints after taking a two-week break from competition, much of that time without touching a club. He holed an eagle putt and made six birdies to offset a few mistakes for a 64, leaving him tied with Thomas Detry.

“It’s a great start, and I would have taken it before I teed off,” McIlroy said.

Riley played in the afternoon when the wind got a little stronger and took as much pride in his par putts as some of his seven birdies.

Riley already has one eye on next week, his Open debut. He narrowly missed out last year and clinched a spot when he shot 66 in the final round at Bay Hill, which offered three Open spots to top finishers.

Riley first came to Scotland in 2014 as part of the Junior Ryder Cup team. That wasn’t on a links course, and The Renaissance Club has only the look of links — it’s not true links soil. It’s still not a bad test for what awaits at Royal Liverpool.

Collin Morikawa credited his experience at The Renaissance Club to helping him win the Open in 2021. Riley could sense and feel how to flight shots and use the ground.

“It’s so much different than playing golf in the States,” Riley said. “It’s just so much fun, flighting shots, maneuvering it with the wind and playing slopes, a part of the game that I really enjoy.

“As firm as it gets, you can utilize some slopes. That’s the best part about it is there’s a million different ways to hit the shot right and that’s what’s so fun about it. That part today, I enjoyed, and that was a big part of the reason I played well.”

He has been looking for momentum anywhere he can find. His season got off to a slow start until he won the Zurich Classic — the lone team event on the PGA Tour — in New Orleans with Nick Hardy. In his eyes, Riley had his second straight round of 7 under par. He shot a 7-under 65 in the final round of the Rocket Mortgage Classic two weeks ago.

“I’m just trying to take that and carry it over,” he said. Riley managed just that on a course nothing like Detroit Golf Club in a town nothing like Detroit.

McIlroy is playing the Scottish Open for only the seventh time as a pro dating to 2008. He has yet to finish in the top 10, and he missed the cut at The Renaissance Club in 2021.

“I haven’t had particularly great experiences around this golf course the last couple times I’ve played,” McIlroy said. “But I feel like my game is definitely in better shape than the last couple times I have played the Scottish Open. Great start. Controlled my ball nicely.”

Detry qualified for The Open in final local qualifying at a links course and referred to this place as his “home garden.”

Max Homa and Tom Kim were among those at 66, while Rickie Fowler was in the group at 67 in his first start since winning in Detroit.

Justin Thomas decided to switch to a cross-handed putting grip on his final nine holes of the Rocket Mortgage Classic (he missed the cut) and stuck with it. The move worked well enough for him to scratch out a 68, joining the likes of Scottie Scheffler and Matt Fitzpatrick.

For some players, a warmup for The Open could be a short one.

Defending champion Xander Schauffele shot even-par 70 and will start Friday outside the cut line. Patrick Cantlay and Jordan Spieth were at 72.