The mechanical watch radiated coolness, much like its owner. It was a constant companion to Newman’s left wrist in magazine shoots, paparazzi photos and while he was speeding around in his race cars. The model, which was “made famous by him thanks to this very timepiece,” was eventually nicknamed the “Paul Newman Daytona,” Phillips Auction House said in a news release.

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After spending years out of the spotlight, the watch landed at Phillips, the auction house, earlier this year. Anticipation grew, as experts speculated it would sell for around $1 million, a high asking price for any watch, even one associated with “Cool Hand Luke.” On Thursday, it sold for $17,752,500 after a 12-minute bidding war.

That’s the world record for the most expensive watch ever sold at an auction, according to Phillips. A portion of the proceeds went to the Nell Newman Foundation.

The watch came to the auction house by way of James Cox, who dated Newman’s daughter Nell for many years. He received it unexpectedly in 1984 while helping Newman repair a treehouse.

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“Paul asked me what time it was, to set his watch. I replied, ‘I don’t know — I don’t have a watch.’ He was clearly surprised. So he said, ‘Here, here’s a watch. If you wind it, it tells pretty good time,’” Cox told the Wall Street Journal. “At that time, I knew Rolex was an amazing brand, but I had no idea how significant the watch was.”

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It was a gift from Newman’s wife, one he only gave away because she had given him a new one. In many ways, it was a symbol of the lifelong love and commitment Newman shared with his wife, actress Joanne Woodward.

To understand the meaning of the watch, one must first understand their marriage.

As the story goes, Newman and Woodward had the same agent, and they met when they both ducked into his office to escape the New York City heat in 1953. That year, they became friends on the set of the Broadway play “Picnic,” but Newman was married. Things were never romantic — Newman watched as Woodward dated Marlon Brando. He set her up with actor and screenwriter James Costigan, to whom she was engaged for a spell.

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Four years later, they were serendipitously cast as lovers in 1958’s “The Long, Hot Summer.”

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When the filming ended, Newman and his first wife divorced. For that, he said he felt “guilty as hell . . . and I’ll carry it with me for the rest of my life,” according to his biography “Paul Newman, A Life.”

Months later, he married Woodward.

Newman and Woodward by all accounts had a wonderful marriage. It would go on to last 50 years, ending only when Newman died in 2008.

And though Hollywood relationships often end in headline-splashing infidelity, Newman reportedly never strayed. When asked by Playboy how someone as desirable as Newman remained faithful, he famously responded, “I have steak at home; why go out for hamburger?”

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Author and journalist Carol Ross Joynt once met the couple at a wedding party in the 1970s. A string quartet played, while guests sprawled out on a large lawn — including the famous couple.

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“Up behind me, Joanne Woodward sat on the ground with her back against the trunk of a big tree, her legs stretched out in front. In her lap rested the head of Paul Newman, who occasionally reached up to touch her face and hair as he savored the music,” Joynt wrote. “It’s possible I gaped. To this day it’s the most romantic thing I ever witnessed.”

Decades later, “Baby Driver” actor Ansel Elgort had a driver who once worked with the couple. He told Town and Country that his favorite passenger was Newman.

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“He asked me about myself, but also he had his wife in the back seat, and this guy was like 80 and he was making out with his wife. They were just PDA and they were giggling and his arm was around her and he’s kissing her,” Elgort said. “I want to be 80 and have a wife who I’ve been with for that long and be that way.”

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But the couple made it sound simple.

Woodward said, “We were good friends before we were lovers . . . We could talk to each other, we could tell each other anything without fear of ridicule or rejection. There was trust.”

Newman was a little blunter, opining that a good marriage required, “some combination of lust and respect and patience. And determination.”

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More than a decade into their marriage, though, the two hit a speed bump when they starred together in the 1969 film “Winning.” It was about a race car driver named Frank Capua, who wants to win the Indianapolis 500 but runs the risk of losing his wife, played by Woodward, along the way.

To train for the film, Newman got lessons in stock car racing. He quickly fell in love with the sport and decided to take it up, first as a hobby and later as professional.

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Woodward was not pleased.

“She skipped his racing practices as often as possible, and when she did show up at trackside in Indy, she couldn’t decide which was worse: the prospect of him killing himself in a crack-up or the clutches of screaming women holding up signs pleading ‘Paul Please Slow Down’ and clucking over him as he walked around the set,” Shawn Levy wrote in his biography.

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“I wish I wasn’t married to him now,” she once told a reporter at the track.

Even so, she supported him. Partially to show that support, she gave him the Rolex Daytona watch as a gift. It carried an important message. On the back face, she engraved the words, “DRIVE CAREFULLY ME.”

That didn’t mean she liked his racing.

“She thinks it’s the silliest thing in the world,” Newman said. “It’s also very scary to her, and she doesn’t much care for it.”

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But she supported him anyway, coming to some of his races so long as he attended the ballet with her. Her support, to Newman, was a symbol of their union.

He wore that watch on his wrist for decades after.

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“[My wife] has always given me unconditional support in all my choices and endeavors, and that includes my race car driving, which she deplores,” Newman once said. ” To me, that’s love.”