PORTRUSH, Northern Ireland — The co-leaders of the British Open entering the weekend at Royal Portrush are both somewhat unlikely candidates.

J.B. Holmes entered the week with five missed cuts and a withdrawal in his past seven tournaments and, other than a win at the Genesis Open in February, has had a miserable season. Shane Lowry entered the week having missed the cut in his past four British Opens.

Yet there they were through 36 holes, standing on 8-under with a one-shot lead over the field.

“Four weeks ago, I thought my career was over … or felt like it,’’ Holmes said. “I struggled. I kind of had two-way misses and struggled getting my club path to be left enough.’’

With so much focus on Northern Irishmen Rory McIlroy and Graeme McDowell, the Irish Lowry was somewhat forgotten among the locals in the field this week.

“If they had offered [the 36-hole lead] to me at the start of the week I would have taken it,’’ Lowry said. “I’m really happy to be where I am. There’s not too many days like that on the golf course. It’s hard to describe. Hopefully, more of the same [Saturday] and see where it leaves me.’’

Asked when he might think about winning, Lowry said, “You start thinking about it when people start asking you about it.’’

“Look, I’m obviously going to be thinking about it,’’ he said. “There’s no point in shying away from it. I’m in a great position. But, my God, have we got a long way to go. There’s two rounds of golf on this golf course against the best field in the world.’’

One person rooting hard for Lowry is McDowell, who said: “[I’m] proud of Shane the last couple of days. I really hope he can keep it going. I’d say Shane Lowry is probably one of the most competitive people I’ve ever met in the life. When he’s under the gun he knows what to do, and he’s not scared. And I certainly wouldn’t put it past him to put his name on that trophy. I’d be very proud of him.’’

McDowell, the Portrush native and unquestioned fan favorite this week, made the cut on the number at 1-over after shooting 2-over in the first round thanks to a triple bogey on the final hole.

“Anytime you’re trying to make a cut on a Friday afternoon, especially at a major championship, you’re always a little tight, a little nervous,’’ McDowell said. “But this one obviously means a lot, to play the weekend here. Just how much this meant, how symbolic this weekend is and to make sure I was in there was very important to me. It was satisfying. I’m proud of myself to reset and get the attitude right after [Thursday’s triple-bogey finish].’’

Darren Clarke, who has a home in Portrush and grew up about 30 minutes away, failed to make the cut after shooting 3-over 74 Friday following his even-par start. It was a particularly heartbreaking missed cut considering Clarke was standing on the 18th tee at even par and tripled the final hole.

“There’s no words,’’ McDowell said. “I’m gutted for him. I know how much this place means to him. He’s been probably the most pivotal of the three [Northern Irishmen in the field] — Rory, myself and him — just because he was the first guy to win a Claret Jug. He’s made his home here. He’s spent more time here in the last 20 years than any of us put together. I’m hugely disappointed for him.’’

With Tiger Woods (6-over) and Phil Mickelson (8-over) missing the cut, it marked the first time in the 83 majors in which they’ve played together that they both failed to make it to the weekend. … David Duval, following his nightmarish opening-round 91 with that 14 on the par-5 seventh hole, closed with a 78 to finish at 27-over par. … Brandon Wu, the 22-year-old amateur from Scarsdale, followed his 2-over-par 73 in the first round with a 76 to miss the cut at 7-over. … Defending champion Francesco Molinari, who opened with a 3-over 74 Thursday, rallied to make the cut on the number with a 2-under 69 to finish 1-over. … Reigning U.S. Open champion Gary Woodland failed to make the cut, finishing at 3-over.