Tina Fineberg for The New York Times

The other day, Glyna Aderhold, a retired 67-year-old real estate broker from Nashville, was crossing the lobby of the mall at the Time Warner Center, the soaring castle of commerce and culture at Columbus Circle, when she passed a monumental bronze sculpture of a man and saw something that made her pause.

“I walked up and I was looking at his head and boom! This thing hits me right in the face,” Ms. Aderhold said.

The thing was the statue’s genitals, which are uncovered and at eye level to the adult viewer. She was being metaphorical. They didn’t actually strike Ms. Aderhold in the face. But they could have.

Ms. Aderhold kept walking, but all day long, shoppers and tourists alike stop at the bubble-figured 12-foot-tall Adam by the Colombian artist Fernando Botero that greets visitors and provides perhaps the most memorable Manhattan meeting spot since the clock in the Biltmore Hotel. And when they stop, they often touch, grasp, pat or rub the statue’s small but prominent penis, while a friend or relative takes a photo.

Grab. Smile. Click. Next.

Just on the other side of the Williams-Sonoma store stands Adam’s partner, Eve. She gets her share of attention, too, but not as much physical contact.

Most of Adam is a deep dark brown; his penis, though, is worn golden from extensive handling.

This is a maintenance issue at the mall. “We have an art dealer that comes in and redoes the patina from time to time,” said David Froelke, the center’s general manager, “but it doesn’t last very long.”

David Benrimon, a New York gallery owner who has sold many of Mr. Botero’s works, said that the artist did not intend for his sculptures to be touched. Management at the Time Warner Center, however, welcomes patrons to interact with the Boteros — imposing, yet playful and approachable in the artist’s signature style — as they see fit.

“In looking at my shoppers coming into the Time Warner Center,” Mr. Froelke said, “there’s so much hustle and bustle that if I can do something to slow the experience down and make it more pleasurable, I’m doing something to make their day a little bit better.”

Around the world and throughout history, of course, people have rubbed statues for luck, from Abraham Lincoln’s nose in Illinois to Lou Costello’s shoe in Paterson, N.J., to the snout of the Porcellino boar in Florence to various parts of the charging bull of Wall Street.

Sculptured phalluses, in particular, are associated with fertility and power. The genitals of hermai in ancient Athens were anointed with olive oil, while farmers worshiped the improbably endowed god Priapus in hope of a more bounteous harvest. In India and Nepal, people touch, kiss and offer rice and flowers to lingams, believed by many scholars to represent the god Shiva’s penis.

People touch and pose with Adam’s penis for many reasons. Because it’s unusual. Because it’s funny. Because it’s just the right combination of naughty and not-too-naughty. Because it’s not in a museum but in a shopping center, where the goods are meant to be handled.

“In our normal lives, you really can’t go up and touch someone’s genitals,” said Fernanda Bennett, the deputy director of the Nassau County Museum of Art on Long Island, which has exhibited its share of Boteros over the years. “But you can if it’s made of bronze and in a public space, and your friend will take a picture of you, too.”

Or as Christian Rosario, 16, a student at Manhattan Theater Lab High School, said after encountering Adam: “It’s a penis, like, in the middle of a mall, just out in the open! It should have a sign on it saying ‘Touch me.’ ”

Within half an hour on a late September afternoon, Adam’s organ drew a steady stream of visitors. First Graciela Fabres, 26, of West New York, N.J., parked her stroller and held her hand beneath the penis, palm up, as if presenting merchandise on “Let’s Make a Deal,” while her husband took her picture. A fiftysomething woman with blond hair and workout clothes grabbed it appraisingly, shook her head with a slight scowl, and walked on.

Then the Yerkinbekova cousins, finance students from Kazakhstan, showed up. Zhanel, 23, grabbed Adam from above, below and sideways, while her cousin Maria, 24, snapped photos. They switched places. Maria kept her distance from the organ.

“I don’t want all our pictures to be the same, both touching the same penis,” she explained.

Some visitors come to Adam with certain ambitions.

“I thought it would be good for sex,” Guenter Virtel, a German tourist in his 40s, said after his wife took a photo of him holding the penis. When Marie Helene Pollett, 65, visiting from France, touched the penis, her son Bruno Pollett explained that she did it for her husband, Jacques, who is 69.

“The luck is for him,” Bruno Pollett explained, smiling at his father. “He will benefit.”

If nothing else, Adam offers visitors to the mall an unmissable landmark. Jack Kelly, a man in his 60s from West New York, N.J., said that he regularly met a friend at Time Warner Center. When they make their plan, do they say, “Meet me at the Botero”? No. Do they say, meet me beneath a certain part of the sculpture? Yes.

“We never get lost,” Mr. Kelly said.