By Martyn Herman

LONDON (Reuters) - When Mike Bryan's cellphone rang recently and the policeman on the other end of the line told him his home security alarm had gone off one thought flashed up in his head -- is my Olympic gold medal safe?

The golden medallion, the one he earned with twin brother Bob at London 2012, is his most prized souvenir from a trophy-laden career that has earned the 38-year-olds 112 titles together, including 16 grand slams.

"We thought someone had broken in, the cops went over and I just said 'dude, please just check that one spot' just make sure it's there. It was there,'" the right-handed half of the most successful doubles team in men's tennis history, told Reuters at Wimbledon, scene of their Olympic glory.

"It's the only thing I hide when we leave for a trip."

No wonder. Bob describes their victory in London as their "greatest moment" while Mike says missing out in Athens, when they were expected to medal, ranked as a low.

They won a bronze in Beijing.

Rio, where they will play with gold-painted rackets, will be Olympics number four -- and the last.

Retirement is looming and they want to sign off in style, perhaps with a golden chest bump.

"(Rio) would be a hell of a way to go," Bob, who juggles life on Tour with wife Michelle and three young children.

"We know Rio will be our last Olympics, I can safely say that. It's been a huge priority. When we sat down to plan the year in December we said peaking for Rio was the goal. Winning in Rio would mean everything."

No retirement decision has been taken, says Mike, but "the conversation" could happen depending on what Rio has in store for the hugely-popular California-based brothers whose victory 'chest bump' had become their trademark.

"You have to earn your way off the Tour, and you have to blast your way out," Mike said. "No one wants to limp their way off. (Pete) Sampras had the perfect send-off.

"He won the U.S. Open and said goodbye."

Amiable off court, a well-oiled machine on it, the Bryans have carried men's doubles for more than a decade.

Ten times they have ended a year as top dogs and have held the number one ranking together for close to 450 weeks in total.

Watching them play is a study in fidgety synchronization.

They are used to being 'hunted' wherever they play, but the Olympics is a whole different ball game with players who usually shun doubles pairing up.

NOWHERE TO HIDE

Roger Federer, Andy Murray, Novak Djokovic and Rafael Nadal will all play doubles in Rio -- Wimbledon champion Murray partnering brother Jamie who was recently ranked one in doubles.

"London was the toughest title we've won, we were so pumped," Bob says. "There's nowhere to hide in the Olympics, right from round one. You got all the great singles guys, the doubles guys, all the top stars."

"The big four want a medal. No one is gonna give it a half-arsed effort. Gold is a gold," adds Mike. "That's going on the medal board for your country. It's going to be a stacked field."

While golf has hit the headlines after a slew of Rio no-shows, and several tennis players including the Bryans' fellow Americans John Isner and Sam Querrey will be absent, the brothers' eyes light up just thinking about the Olympics.

"It's bigger than the game of tennis," Mike said.

While Bob added: "I remember after London it didn't hit us until about two weeks later when we were driving in Cincinnati. Then I sought of yelled "Yeah" at the top of my lungs."

"We were like 'Oh man! this is nuts'. We ended up having one of the best summers of our career."

So popular were the medals that Mike described his as a 'celebrity' in its own right while Bob's was so in demand it picked up numerous battle scars.

"When I took the medal out people flocked to it," Mike said. "It was wild. It was like Lord of the Rings. It was crazy."

Bob even did the dirty on his brother.

"His was all shiny, the ribbon was perfect so I did a switcheroo," he said. "He didn't realize until next year!"

Whatever happens in Rio their careers will be forever entwined -- it's either together or never.

"You could go and make some dough with someone else," Bob teases his brother, "Just cut me in."

"No, no, we are a package deal. "We came in together we'll go out together," Mike says.

(Editing by Pritha Sarkar)