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Of course that's one way of proving this wrong. But you have to start above 18 quadrillion. Because all the numbers less than that have been tried.

Has anyone tried really, really large numbers picked at random?

One approach. But I'd suggest it has less than a one-in-18-quadrillion chance of working. From the statistics so far.

It's trivial to do. Here: https://js.do/code/383036