Let's start with a simple, astounding fact. In the 68 years after Hiroshima and Nagasaki, apart from scheduled nuclear tests, not a single nuclear warhead has exploded. The remarkable thing is not that nuclear weapons have never featured in a hot war. Basic human sanity – awareness of the devastation that would be caused by today's far more powerful devices – has ensured that. What is truly astonishing is that since 1945, no nuclear weapon has gone off by accident.

Today the topic, here in the United States or among the original nuclear powers, seems almost irrelevant. We take atomic weapons for granted. Not so perhaps in the Middle East, or in the Indian subcontinent, or North Korea. But we British, Americans, Russians, French, and Chinese have virtually forgotten about them, certain they will never be used in anger.

Not that they no longer exist. The US, according to the Center for Arms Control and Non-Proliferation here in Washington, currently has around 4,650 strategic missiles, 1,950 of which are deployed, the rest on stand-by. No figures are published, but upkeep, support and modernisation of the nuclear force reputedly costs at least $50bn (£31bn) a year.

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Drive across the plains of North Dakota, Wyoming or Montana, and you might notice the odd small gravelled area by the road, with some gadgets protruding from the earth, protected by barbed wire and ferocious "Keep Off" signs. You might think it is an electricity sub-station. In fact you are passing one of 450 concrete silos on the northern plains that contain a Minuteman III intercontinental ballistic missile (ICBM) with a single warhead, each capable of obliterating Hiroshima 27 times over.

That however is as physically close as ordinary punters will ever come to America's nuclear deterrent. The rest is aboard bombers within the sealed perimeters of vast air force bases, or hidden beneath the ocean on 14 Trident submarines – out of sight, and entirely out of mind.

But it was not always thus. If you want an idea of what might have been, read Eric Schlosser's enthralling Command and Control, that weaves together the post-1945 history of the US deterrent with a frame-by-frame recreation of the country's most celebrated brush with accidental Armageddon.

It happened back on 18 September 1980 at a missile silo in rural Arkansas. The silo contained a Titan II fitted with a W-53 warhead, the most potent in the US arsenal, with a 9-megaton yield, 600 times more than Hiroshima.

A worker doing routine maintenance dropped a spanner that fell into the silo and ruptured the missile's fuel tank. Fumes swiftly built up in the confined space. Nine hours later the Titan II blew up, utterly destroying the silo and sending its 740-ton launch closure door spinning into the night sky and depositing the warhead 50 yards away. The safety devices held and it didn't go off, but one person was killed and 29 injured. Local residents had been evacuated – but much difference that would have made, had the worst occurred.

In his researches, however, Schlosser unearthed a yet more terrifying nuclear near miss, 19 years earlier. In January 1961, a B-52 carrying two hydrogen bombs broke up in midair over North Carolina. The bombs came to earth amid the wreckage, and on one of them three out of four automatic arming mechanisms had gone ahead. Only a last safety switch held, preventing a calamity that would have wiped out or rendered uninhabitable much of the East Coast. In comparison, the Cuban missile crisis was a virtual non-event.

And this was just one of at least 700 significant "incidents" between 1950 and 1968 in the US. You wonder how many others went unreported. Imagine, too, the brushes with disaster there must have been in the Soviet Union during the period. But as far as we know, none ever produced an accidental, full-scale nuclear detonation.

Since then, thanks to diminishing stockpiles and improved safety procedures, such "incidents" have been far fewer. But never rule out the human factor. Somehow, for example, in contravention of rules set in place after North Carolina, six cruise missiles fitted with live nuclear warheads were carried on a flight in 2007 from North Dakota to Louisiana without authorisation. Apparently, loaders confused dummy warheads with the real thing.

And even in these past couple of weeks, human frailties have made one wonder. In one bizarre episode, the three-star admiral who was the second ranking officer at US Strategic Command, whose brief includes the country's nuclear strike forces, was removed from duty after being caught using counterfeit poker chips at a casino at Council Bluffs, Iowa just across the river from Strategic Command's HQ at Offutt Air Force base in Omaha Nebraska.

A few days earlier, Major General Michael Carey was sacked from his command of the 20th Air Force, responsible for those Minuteman III missile silos in North Dakota, Wyoming and Montana, and their launch centres. Both instances involved "unfortunate personal behaviour", a senior Pentagon official told the Associated Press news agency, stressing however that the country's nuclear deterrent force was "safe, secure and effective".

But new revelations last week make one wonder. Earlier this year, two of the three nuclear wings under the 20th Air Force performed badly in a safety and security inspection, and 17 military personnel were made to undergo retraining. Moreover, on two occasions doors to launch control centres were left unlocked, in breach of regulations, AP reported – on one occasion when an on-site food order was being delivered. Of course the guy from Domino's Pizza can't just wander in off the street and press the button, but even so ….

Such is the surreal banality of America's nuclear weapons today. No wonder morale is said to be poor at the ICBM sites, in the rearmost line of battle, of a war that will never be fought. Back in the 1960s, 1970s and 1980s, at the height of the Cold War, the greatest nuclear threat to America was accidental detonation of an American weapon. That remains the case now. Let's hope the dumb luck holds.