I'm using a Galaxy S6 with Android 5.1.1 Unrooted.

Whenever I turn BOINC on, it runs the task for maybe a couple of seconds before suspending it for a couple seconds, it does this the whole time I have it running.

Plugged in, not plugged in?
If plugged in, what is the minimum battery level you set that the phone should have before BOINC is allowed to rock&roll?
Is the phone at that time at that level, dipping under it when running work, charging again to above it, then continuing work?

Is by chance your maximum battery temperature met?
Do you have "Pause at CPU usage above N%" set to a low value, or is this level met by non-BOINC programs during your run?
What is the value for CPU Limit? Anything less than 100% will do a thermal throttle.

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What about the CPU time setting? Since it's only a few seconds of pausing maybe the CPU time setting is less than 100%.

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Hallo together,

I'm also running boinc on Samsung Galaxy S6. Even though there is no GUI since short after I've registered the projects, jobs are still running.
If the device is plugged by the original charger, it's running without interrupts. At this time the green LED shows 100% Battery capacity short after it reaches minimum battery level. If it is connected by USB (2.0), most time there are a lot of interrupts in crunching when the device gets about minimum battery level. The red LED says that the device all the time is charging, but never leaves minimum battery level significant.

This behavior is because of boincs energy consumption. The original charger delivers enough energy for crunching, USB (in my case 2.0) does not. Perhaps USB 3.0 or the following USB standard has more power.

Same behaviour on my nexus5 with 6.0. It doesn't matter if plugged in or not or what settings I use. As long as I put CPU limitation below 100% the tasks run for 2 seconds, then stop for 2 seconds and so on. Using different cores doesn't help. Right now 1 core with 100% works for me but I don't think this is the right behavior. Temperature is set to 40 (is 35 right now) and battery is set to 80% (is 99% right now)