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That is a very good question!
There are 2 parts to the answer, one part about BOINC and the other part about the Gridcoin client.
The science work runs on a platform called BOINC, the BOINC manager that gives you control over that is extremely lightweight, it runs on my Android phone and on a Raspberry Pi with hardly any resource usage at all. The science work that you are processing, the tasks or as we call them the Work Units, can use upto 100% of the rest of your devices available CPU, unless you set a lower limit. Each task or Work Unit has a deadline by which it must be returned completed, most projects allow quite generous timescales, so you do not need to run 24 hours on high power equipment to complete them in time.
Gridcoin is a separate application, it too uses very little CPU time and again it does not need to run 24 hours, you could run it just once a week for a day to catch your rewards. On my Raspberry Pi 3 Gridcoin uses about 30% of one CPU core, on my big PC it uses about 3%.

So you can see from that, you can use very low power/old equipment and all it does is add to Gridcoin and the scientific work being done. I personally have not heard of anyone being unable to run it.

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