The virtual monkeys, created by an American programmer, have already typed up the whole of the poem A Lover's Complaint and are 99.99 per cent of the way through the Bard's complete works.
The experiment attempts to prove the theory that an infinite number of monkeys sitting at an infinite number of typewriters would eventually reproduce the works of Shakespeare by chance.
Jesse Anderson, the programmer behind the project, said he was inspired by an episode of The Simpsons which spoofs the famous problem.
Mr Anderson set up millions of small computer programmes, or virtual monkeys, using Amazon's SC2 cloud computing system, and programmed them to churn out random sequences of nine characters.
If the nine-letter sequence appears anywhere in one of Shakespeare's writings, it is matched against the relevant passage in a copy of the Bard's complete works, and is checked off the list.
The monkeys, which started typing on August 21, have already completed more than five trillion of the 5.5 trillion possible nine-letter combinations, but have so far only finished one whole work.
But the experiment is an imperfect reproduction of the infinite monkey theorem because it saves correct sections of text while discarding future wrong guesses, experts said.
Dr Ian Steward, emeritus professor of mathematics at Warwick University, said that for the monkeys to type up the complete works in the correct order without mistakes would take much longer than the age of the universe.
He told the BBC: "Along the way there would be untold numbers of attempts with one character wrong; even more with two wrong, and so on.
"Almost all other books, being shorter, would appear (countless times) before Shakespeare did."
Writing on his blog, Mr Anderson said: "This is the largest work ever randomly reproduced. It is one small step for a monkey, one giant leap for virtual primates everywhere.
"I understand the definition of infinite and infinite monkey theorem and I realise that this project does not have infinite resources.
"No monkeys were harmed during the making of this code. This project is my attempt to find a creative way to attain an answer without infinite resources."
In 2003 the Arts Council for England paid £2,000 for a real-life test of the theorem involving six Sulawesi crested macaques, but the trial was abandoned after a month.
Read more at The Telegraph
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