Gamma-ray pulsar search #2 v1.12, LATeah0041U_1392.0_1676400_0.0

This is not a problem or issue at all. It's just the way BOINC works. Your computer is quite ancient and (I assume) is using hyperthreading to give 2 'virtual' CPUs. If so, this will give better overall performance (two tasks crunching simultaneously) but each thread will be quite a bit slower than if crunched on a 'real' CPU. BOINC has probably come up with a rather optimistic view of how long a task is likely to take to run to completion. As processing progresses, BOINC will continually update its estimate of the remaining time and because the real crunch time is going to be a lot larger than the original estimate, the current estimate will be continually growing.

Eventually, perhaps when crunching is close to completion, the estimate of remaining time will be much more accurate. It will then start decreasing as you would expect.

You should perhaps delay updating until such time as you are ready to do it. That way you can ensure BOINC is stopped while an update is in progress. I would imagine that the update process itself should take proper care to stop and restart other processes but if you think that is the problem you could always take control yourself.

Your computer shutting itself down randomly could also be a sign of overheating. Years ago, I had a hyperthreaded P4 that used to do that. You should inspect the condition of your CPU heat sink and fan. If they are clean and free of dust and fluff buildup, it could be the thermal interface material (TIM) between the heat sink and the top of the CPU. You may need to clean it away and apply new thermal grease.

You can get a good idea if the problem is heat related by running a utility to monitor CPU temperatures. I've used one called Core Temp, but there are many others freely available. Do a google search.

A computer shutting down may not be just due to excess heat. It can also be caused by bad power. Both PSUs and the power regulator circuitry on motherboards can suffer from degrading of components like capacitors due to heat over time. If you can see signs of 'swelling' of capacitors, that is likely to be the problem. Your computer may run quite normally when lightly loaded. The extra heat and stress of crunching could be what is causing it to quit. This is increasingly likely with older components.

Inspect and thoroughly clean the inside of your computer. Pay particular attention to blocked fins on the heat sink. Remove the fan and clean everything thoroughly. Use something like a small paint brush to get into crevices and loosen the dirt. Blow out thoroughly. Check the fan for freedom of spinning. Check all the capacitors on the motherboard for signs of leakage or swelling. The most likely ones tend to be in a group quite close to the CPU socket.

When you restart the machine, run a temperature monitoring utility and record temperatures, both when idle and when running at 100% load. In fact, you should do this both before and after cleaning to see the difference. If you don't get a significant improvement, you should consider replacing the TIM. Computer stores will stock a range of suitable products. Do a google search for "How to apply new thermal grease" to get detailed instructions.

Good luck with identifying the cause of the shut down.