Ayn Rand and Unknown Quote

In a YouTube clip, Ayn Rand is being interviewed by Tom Snyder and she says the following: ‘What I’ve always thought was a sentence from some Greek philosopher – I don’t, unfortunately, remember who it was – that I read at 16, and it’s affected me all my life: "I will not die. It’s the world that will end."’.

Does anyone here know which Greek philosopher she was quoting? Google reveals nothing. Thanks.

Sounds like a paraphrase of something Gorgias might have said.