By Christian Fraser
BBC News, Naples
Vesuvius is the most heavily monitored volcano in the world.
Experts warn that Naples is within range if Vesuvius erupts
Within 20km (12 miles) of its crater live almost three million people - and every one of them, say the geologists, is at risk.
Their evidence comes from research, now completed, which shows that 4,000 years ago Vesuvius erupted with such ferocity that huge areas of land around the volcano were uninhabitable for decades.
Geologists say the evidence that has been uncovered since 2001 should have encouraged Italian authorities to change the evacuation plan they are rehearsing.
But vulcanologist Giuseppe Mastrolorenzo from the Vesuvius Observatory says civil emergency planners are still ignoring the worst-case scenario.
"It is politically negative to talk about the cataclysmic event," he says.
"The authorities have been told what could happen. But the evacuation plans they have in place still do not go anywhere near far enough."
Avalanche of ash
Mr Mastrolorenzo and his team took us to a disused quarry not far from Naples where they have been busy collecting samples.
The walls are made from solidified ash, at least 20m (66ft) high. Over thousands of years this ash has solidified into porous rock.
It is the deposit of a Stone Age eruption, a cataclysmic, Plinian eruption, much bigger than the type that destroyed Pompeii in 79AD.
When the volcano exploded, it sent a cloud of superheated dust and ash high into the stratosphere, which eventually collapsed over a radius of 25km (15 miles).
The avalanches of hot ash raced down the slopes of the volcano at several hundred kilometres an hour, destroying everything in their path.
Within the city of Naples they found deposits of this ash up to 3m (10ft) deep.
"We have found footprints of people trying to escape," says Mr Mastrolorenzo.
"And a Stone Age house with plates of food abandoned in a hurry. As they ran they were pelted with rock that was falling from the air.
"Before we made this discovery we had no idea the city of Naples would be threatened. We never had evidence for a blast extending into the Neapolitan area and beyond it."
From a helicopter we could see the difficulty the civil planning authorities will face.
The slopes of the volcano are covered with farms, small towns and high-rise flats.
Beneath Vesuvius' crater is a vast chamber of molten magma
The so-called "red zone" - the area that would be evacuated first - includes 18 towns. And they are connected by narrow, winding and often heavily congested roads.
Guido Bertolaso is the head of civil protection and in the past few months his team has been practising with residents and local authorities the evacuation routine.
"In any situation where civil protection is involved there is always a criticism," he said.
"We work knowing full well that the entire region will be affected. We know what to do. Our big challenge is communicating that to the local people."
The plan assumes at least 600,000 people would need to be evacuated. It would take 72 hours and the evacuees will mostly be sent to other parts of the country.
But the experts say the evacuation plan should include Naples, and they believe people in the city are not adequately prepared for what would unfold.
Tests on the volcano show Vesuvius is a ticking time bomb. Ten kilometres beneath its crater there is a 400 sq km chamber of molten magma.
When it forces its way through the fractures of the Earth's crust the result will be disastrous.
Vesuvius is regarded as one of the world's most dangerous volcanoes
The authorities would get between 20 days and two weeks' notice. But the dilemma that would face those implementing the plan is when to start their evacuation.
In San Sebastiano, a town that was partially destroyed in 1944 by the lava from the last eruption, one elderly resident, Giuseppe, told me he believed he would have plenty of time to go.
His memories are of a lava flow that moved at 5km/h.
"Last time it all happened very slowly," he says.
"And then it stopped. We are not afraid. We left briefly in 1944 and then we came back to our houses."
But there will be no quick return if Vesuvius erupts as it did 4,000 years ago.
When this next explosive, Plinian eruption comes - as one day it will - this will not just be Campania and Italy's problem, it will be Europe's as well.
There will be three million refugees. It will change climates and weather patterns across the continent.
And it will turn the green, fertile landscape around Naples into a lifeless desert, to which Giuseppe and his friends will certainly not want to return.