GIMPS has just announced that $2^{136,279,841}-1$ is prime. Does anyone have a sense of the scale of the computational resources involved in finding this? (And maybe how it compares to, say, training AI models or mining bitcoin).
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3$\begingroup$ Do you mean the amount of total computation since the last one, or the amount to just check this one number is prime? $\endgroup$– David Roberts ♦Commented Oct 21 at 20:29
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6$\begingroup$ I’m voting to close this question because it's more suitable for cs.stackexchange.com $\endgroup$– Max AlekseyevCommented Oct 21 at 21:04
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3$\begingroup$ If nothing else, this thread mersenneforum.org/node/1055976/page12#post1057519 should be an interesting read - it's the (12 page) discussion between the first detection of the prime as a probable candidate, and now. $\endgroup$– David Roberts ♦Commented Oct 21 at 23:13
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2$\begingroup$ @DavidRoberts Thanks for pointing out that thread! Elsewhere on the GIMPS website, I found the following charts: mersenne.org/primenet/graphs.php. It seems in the last 180 days, on average the project used about 10,000 TFLOP/s. So that gives some sense of the scale. $\endgroup$– RegularGraphCommented Oct 22 at 1:46
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1$\begingroup$ According to Luke Durant himself, it cost close to two million dollars. $\endgroup$– Timothy ChowCommented Oct 22 at 23:16
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Although GIMPS is a distributed computing effort, the computations for the latest Mersenne prime were largely funded by a single person, Luke Durant, who, in an interview, said that it cost him nearly two million (US) dollars.
For comparison, it is estimated that Bitcoin miners are currently mining around 20 million dollars' worth of Bitcoin per day. Assuming that Bitcoin mining is profitable, but not insanely profitable, we can infer that the cost of that mining is somewhat less than 20 million dollars a day.
Training an LLM involves both capital expenditures and computing time. Ignoring the capital expenditures, it is estimated that training Llama 3.1 405B cost about 60 million dollars.
answered Oct 25 at 21:37