Martin Cooper stood in front of the Hilton on Sixth Avenue, clutching an unwieldy hunk of beige plastic that weighed almost 3 pounds. He punched in a nine-digit number, then waited for a telephone 30 miles away — in Murray Hill, NJ — to ring.

The date was April 3, 1973, and the Motorola engineer and his hastily cobbled-together team had just spent five months building a handheld cellular phone.

Forty-five years later, the device that changed the history of technology by making communication as mobile as it had ever been seems like a given; after all, today there are more cellphones on Earth than people.

But at the time, Cooper and his colleagues were nervous.

“Here we were, doing what has turned out to be a historical event. But what was most on my mind at that time was, ‘Is this thing going to work?’ ” said Cooper, now 89 and living in San Diego. “There was an engineer standing about 30 feet away with another phone.”

The backup wasn’t necessary; the first-of-its-kind call connected, and Joel Engel answered the line. Engel headed up a rival group at Bell Labs (then part of AT&T) that was also working furiously to develop cellular gadgets.

“I said, ‘Hi Joel, it’s Marty Cooper.’ And he says, ‘Hi, Marty.’ And I said, ‘I’m calling you on a cellphone — but a real cellphone. A personal, handheld, portable cellphone.’ And there was silence,” Cooper said. “I think he was crying into his teeth. I’m only conjecturing.”

Added Cooper, “I hesitate to use the word enemies, but we were on opposite sides of the landscape.”

The stakes were high. Schaumburg, Ill.-based Motorola, a relative upstart known for manufacturing two-way radios, had one-upped one of the biggest telecommunications companies in the world. Cooper’s call to Engel was a gimmick that paid off. The story appeared in newspapers around the country — including The Post — the next day.

The cellular arms race began in 1947, when Bell Labs engineer Doug Ring wrote an internal memo sketching out his vision for a network in which phones didn’t need to be attached to a wall. In the years that followed, AT&T engineers prioritized car phones; early versions required about 30 pounds of equipment in the trunk plus a nearby cell tower to work. Motorola was working on more mobile tools that, according to Cooper, were inspired by a request from the Chicago police superintendent. Officers needed to talk to each other even after they’d left their patrol cars.

“We thought our vision was right, which was that someday everyone would be walking around carrying phones with them,” Cooper said. “It’s those little details of not having to worry about stuff. The best technology is when you are free to do what you want.”

The two firms battled it out throughout the 1970s, and competition propelled innovation. Cooper’s prototype had a battery five times bigger than a modern cellphone. Those got smaller — and engineers added screens. But regulations didn’t keep pace with the advances in hardware. Because of fights over frequencies and other issues, the Federal Communications Commission didn’t permit the first portable handheld phones to be marketed until 1983 — a decade after that first call.

The bureaucratic delay helped hone the product. “What we built in 1973 was handmade, put together with thousands of parts by engineers. We could keep it working for an hour until somebody had to fix it,” Cooper said. “The reason we picked that dumb brick [design] was because it was simple. Anything we did that was complicated would break while we were demonstrating it.”

During that time, Motorola spent $100 million to create a sturdier phone for commercial sale, according to the company’s then-director of industrial design, Rudy Krolopp. So it was a slightly spiffier version of Cooper’s brainchild that became available to the general public.

The Motorola DynaTAC 8000x was 9 inches tall, contained 30 circuit boards and could store 30 numbers. After charging for 10 hours, it had enough juice to sustain 35 minutes of conversation. The price tag started at $3,999; most plans cost 50 cents per minute. (Today’s market for nostalgia means bidding for one on eBay is currently at $1,960.)

Cellphone technology continued to evolve over the years. Sizes shrank, as did prices.

“From the time somebody thinks up an idea about some complicated technology to the time they produce the first one is typically 20 years,” Cooper said. “From when someone markets the first one to when your neighbor has one is another 20 years.”

Perhaps that explains why the world was a bit slow to grasp the significance of Cooper’s call. The Post buried its story on the Hilton demonstration on Page 72 with the headline “Phone of the Future? 3 pounds and Portable.”

The reporter on that story, Jane Perlez, now the Beijing bureau chief of the New York Times, told The Post, “I had some idea it was pretty ground-breaking.” Perlez remembered making a test call to her family in Australia as part of the demonstration; in the story, she described the experience as a “post-James Bond style of communication.” She said she doesn’t remember Cooper.

He, on the other hand, has built a career out of 1973’s events. A Chicago native born to Russian immigrants who made their living as door-to-door salespeople, Cooper has made cellphones an intractable part of his identity. On a superficial level, his Skype handle is MartyCell; on Twitter, it’s @MartyMobile.

He married another wireless electronics prodigy, Arlene Harris. Together, they’ve founded and sold companies including Jitterbug, which makes big-buttoned, big-screened phones for seniors.

What sticks with Cooper is the wide-ranging consequences of the creation. “The thing I am most proud of is, in Africa, the UN did a study, and a billion people over the last 20 years have moved out of ‘severe poverty’ into what they categorize as ‘poverty’ — mostly as a result of the cellphone,” he said. “That is societal impact.”

Cooper advocates lowering the costs of cellphones and expanding wireless coverage to underserved areas. “We should be focused on how to make people’s lives better,” he said. “That is the purpose of technology.”

Last month, Cooper upgraded his own cellphone to the newly released Samsung Galaxy S9.

Even inventors need tech support: He said it took several hours to set up. While demonstrating his new toy, the digital voice assistant piped up; Cooper shushed it with a “Shut up!”

Tech pioneer or no, he still doesn’t approve of cellphones at the dinner table for his two kids and several grandchildren. But they still astound him.

“The amount of stuff they’ve crammed into there, a supercomputer and seven different radios and three cameras in this cellphone, is amazing. They’re trying to build a universal device that does all things for all people,” said Cooper, who likes to examine the guts of his cellphones to educate himself about the latest techniques. “If you asked me what the most important thing in my life is, it’s learning.”

Today, different giants — Apple, Google, Amazon — dominate the tech industry. But the humble origins of the cellphone are finally getting their due outside the Silicon Valley bubble.

Last year, contemporary artist Doug Aitken spent a few days recording Cooper near his home. In the audio-visual piece, Cooper recounts his breakthrough project in a steady, proud cadence, while Aitken intersperses bass-thumping music and psychedelic patterns. The installation, “New Era,” debuts April 13 at 303 Gallery in West Chelsea. The narration is telling.

“I made a phone call,” Cooper is heard saying. “And it’s just not going to stop.”