Backing for Bletchley Park and Turing papers
The papers, which contain details of his pioneering work on artificial intelligence, are due to be auctioned very soon.
The scientist, who killed himself in 1954, created a machine at to crack messages in the German Enigma code.
Speaking in the Commons, David Cameron said: "Alan Turing was a remarkable man and we all owe a debt of gratitude to those people who broke the Enigma Code."
Turing, who has been called the "father of the computer", published only 18 papers in his short career.
The collection, which contains his first published paper, his pioneering work on artificial intelligence and the foundations of the digital computer, had a guide price of between £300,000 and £500,000. But failed to reach the guide price at auction.
Now a big campaign is underway to raise £300,000 to buy the papers for .
"They've received a lot of private donations, even Google has made a sizable donation," says , who raised the issue at Prime Minister's Questions. "There's no doubt the money will be raised, they just need a little more time to get the funds in place".
So in the House of Commons he asked: "Will my Right Honourable Friend do all he can to secure these important papers for the nation?"
Mr Cameron replied: "I would certainly like to do that... of course, I hope private donors will generously support the fund raising campaign and I'm happy to work with him to do all I can to make it happen."
Mr Stewart hopes that by getting the Prime Minister to back the campaign, it will raise its profile and perhaps encourage a few more people to contribute to the fund - and persuade Christies to delay the auction for a little longer.
Turing was once described by one of our technology colleagues as a "hero for geeks".
He was prosecuted for having a sexual relationship with a man and later committed suicide.
Last year, the then Prime Minister Gordon Brown gave Turing a for the "appalling" treatment he received for being gay.
Now the present Prime Minister is throwing his support behind the campaign to keep his important papers where they belong - back at Bletchley Park.
Welcome to the political blog for the East. I'm Deborah McGurran, the Ö÷²¥´óÐã's Political Editor for the region. From Lowestoft to Luton, this is the place for politics with an eastern twist.
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