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The heir said: "It is a rare privilege to celebrate a century of life.
"But it is rarer still when that person has transformed the way we see the only home that we have - Planet Earth.
"And it is that sense of urgent optimism that has made all the difference."
The prince, who established the Earthshot Prize in 2020, said Sir David has been a major influence on his life.
"To work with those who are raising awareness of the challenges and building the solutions that drive meaningful change.
"Through your support in establishing the Earthshot Prize, we are now striving to turn your inspiration into action, to champion those solutions that are creating a more sustainable future for us all."
The Royal Albert Hall celebration was hosted by Kirsty Young and included performances from musicians who have featured on Sir David's BBC Planet Earth TV series.
