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NancyLebovitz comments on Open thread, Oct. 6 - Oct. 12, 2014 - Less Wrong Discussion
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Should The Great Internet Mersenne Prime Search be considered a bad idea by that measure?
Are there any benefits to knowing prime numbers so large they can't even be used in cryptography?
No?
Then I guess it's a bad idea.
You never know what's going to shake out from pure math. Still, hunting for extremely large primes might not be efficient, even by the standards of pure math.
This is only tangentially my field, but I'd expect the numbers themselves to be much less potentially useful than the algorithms needed to find them. Since GIMPS is just throwing FLOPs at the problem through established math, it doesn't look like an especially good approach to me.
What could be learned by getting to know more of those numbers? What's the benefit of knowing them now over waiting, e.g., 100 years when computing power is cheaper and better algorithms might exist?
And what else could be done with the computing power?
Although you can indeed never know the outcome of research, I think we can estimate whether particular research is worthwhile.