Major conspiracy theories would have been exposed within years if they were really true, a scientist has concluded.
Dr David Grimes, a physicist at Oxford University, has developed a mathematical equation he says reveals how long a conspiracy can survive without being found out.
He applied his formula to four famous "cover-ups" to show the truth behind the rumours.
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"I hope that by showing how eye-wateringly unlikely some alleged conspiracies are, some people will reconsider their anti-science beliefs," he said. "While believing the Moon landings were faked may not be harmful, believing misinformation about vaccines can be fatal."
How does the formula work?
His equation expresses the probability of a conspiracy being revealed, either deliberately or unintentionally. By analysing data from genuine collusions, including the National Security Agency's Prism surveillance programme revealed by Edward Snowden in 2013, Dr Grimes was able to factor in variables such as the number of conspirators and length of time it took for the secret to be revealed.
"It represents a 'best case scenario' for conspirators," says the BBC's Alex Berezow. "It assumes that they are good at keeping secrets and that there are no external investigations at play."
What does the equation suggest about the Moon landings?
The belief that the Moon landings were a hoax has become one of the most persistent conspiracy theories of all time. Sceptics claim that the 1969 landings – and all those which followed – were faked by Nasa and that no human being has ever set foot on the surface.
Using his equation, Grimes was able to calculate that a hoax would have been revealed after three years and eight months, as it would have begun in 1965 and involved about 411,000 Nasa employees.
What about other famous conspiracy theories?
Grimes applied the same formula to three other well-known conspiracy theories. According to his calculations, the climate change "myth" would be revealed in three years and nine months, the vaccine-autism "conspiracy" in three years and two months and the "plot" to withhold a cancer cure in three years and three months.
"In simple terms, any one of the four conspiracies would have been exposed long before now," he concluded.
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