Who has predicted such a thing? Moreover, why would anyone believe it?
There's certainly enough nuclear weapons around to destroy the entire world, but then there has been for donkey's years. The bombs dropped on Hiroshima and Nagasaki were extremely small devices by modern standards however.
For myself, I don't believe anyone has ever made genuine predictions based on an ability to see the future. There's been some lucky guesses, but most of it is stuff like Nostradamus, who is so vague that it's easy to retrospectively interpret it as referring to specific event.
I must confess the thing that worries me about this kind of thing is the people it appeals to - it's like Bush being bankrolled by fundamentalist Christians who are desparate to support any war in the middle east as this will fulfil their notions of armageddon and the second coming of Christ. Self fulfilling prophesy.
On the other hand, I predict this won't happen...