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answers:

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What is the total number of threads that can run concurrently on an nvidia Tesla, say S1070.

A: 

Combining information from NVIDIA's product page with this site and an interesting forum post, I'd say you're looking at 30720 simultaneous threads on an S1070. (4 gpus, 240 cores to a gpu, 32 threads to a warp on each core)

Kim Reece