He was admitted to London’s King Edward VII hospital on Monday, a day after attending the rain-drenched Jubilee river pageant with the Queen.
On Friday, the Duke of Edinburgh was visited by the Duke of Cambridge and Prince Harry, the latest in a series of visits from his family.
Prince Philip will celebrate his 91st birthday on Sunday.
Earlier this week, Buckingham Palace said the duke’s condition had “improved considerably” and that he was being treated with antibiotics and was in “good spirits”.
Clarence House said Prince William and Prince Harry paid a “short private visit” to see their grandfather on Friday.
They made no comment to reporters outside as they left after 20 minutes.
Prince William visited the duke while on leave from his RAF search and rescue duties.
On Thursday, it was announced that he had qualified as a Royal Air Force search and rescue captain, after passing his tests on 29 May.
Meanwhile, his brother Prince Harry – a captain in the Army – has spent this week on pre-deployment training at RAF Wattisham in Suffolk.
The Queen and the Duke of York visited Prince Philip on Wednesday. Prince Andrew said that his father was “mending very well”.
Prince Philip had appeared to be in good health when he accompanied the Queen on Sunday on the royal barge the Spirit of Chartwell, which formed part of the Jubilee river pageant.
His admission to hospital meant that he could not join the Queen at the final Diamond Jubilee events to mark her 60 years on the throne.
Prince Philip is not due to attend his next scheduled engagement until Tuesday, when the Queen hosts a garden party at the Sandringham Estate as part of Jubilee celebrations.
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