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>"Anyone can download the software free. So you, too, could discover a record-breaking prime number — if you have enough patience."

Maybe mining zcash is lucrative, but finding a new big prime number sounds pretty nice

I wish we can collectively "mine" solutions for questions that are currently un-solved.

Like Larger prime number, or create a hive mind that acts as an AI.

Isn't that the point of projects like folding@home?

And hive mind AI is literally skynet.

The Borg would be a better analogy; Skynet was just an AI with a specific purpose, no hive-mind about it.

Well that's more reassuring.

There are attempts to do this, for instance Primecoin and Curecoin.