(CNN) — A great white shark, believed to be one of the largest on the planet, has been spotted by divers as it fed on a whale carcass off the coast of Hawaii.

The divers, who captured remarkable footage of the encounter, say the shark is Deep Blue -- a 20-foot-long female.

The creature approached the team's boat to scratch herself on Tuesday, and was flanked by two "dancing" dolphins as she swam, diver Ocean Ramsey wrote on Instagram alongside a picture of the meeting.

And incredibly, the group got close enough to touch the shark as it passed.

"Deep Blue came up and brushed up against the boat, maybe she's pregnant, maybe she's itchy?" Ramsey wrote, adding: "She swam away escorted by two rough-toothed dolphins who danced around her."

Deep Blue is over 50 years old, and was caught on camera five years ago in a video that quickly went viral.

Ramsey said her team had been monitoring tiger sharks feeding when the legendary great white made her surprise appearance. The divers "spent the entire day with her till the sun went down," Ramsey wrote.

Ocean Ramsey swims next to the great white, believed to be Deep Blue. @OCEANRAMSEY/AFP/Getty Images

"I waited quietly, patiently, observing as she swam up to the dead sperm whale carcass and then slowly to me," she said. "I gently put my hand out to maintain a small space so her girth could pass."

Ramsey touched the shark as it swam by and, while noting that some divers frown upon this, added that "sometimes sharks seek touch."

The species "are not the mindless monsters they are portrayed as," she said.

But Ramsey later warned people that the creatures can be unpredictable, writing: "I highly discourage people from purposely jumping in the water with great white sharks or tiger sharks." CNN has contacted Ramsey for further comment.

Diver Ocean Ramsey swims alongside the shark. Instagram/JUANSHARKS/OceanRamsey

John Richardson, conservation officer at UK organization The Shark Trust, told CNN that the spotting of Deep Blue is "incredibly exciting."

He added: "If Deep Blue does prove to be pregnant, this is even more significant."

"While white shark sightings are rare in Hawaii, satellite tagging shows they make annual migrations from the Californian coast to the middle of the Pacific each winter -- including Hawaii," Richardson said. "While males return to Californian waters, female white sharks often appear to remain offshore."

But he warned against engaging with sharks as closely as the divers did, stressing that the species can be "unpredictable."

"While it's great to see a 'positive' shark-human encounter given global coverage, we must add a note of caution which holds true for interactions with any large, powerful wild animals," Richardson said.