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Anyone know how many transaction per second the Ethereum network can handle?

Also, how fast does the blockchain grow in size in GB/month?

They've hit 8 tx/sec in production and 25 tx/sec on the testnet. Proof of stake should increase capacity to over 100 tx/sec, and a simple sharding scheme to at least 10,000 tx/sec. Long-term they hope to do even better.

Blockchain size is increasing rapidly, I think it's up to 40GB already. But they plan to implement pruning before it becomes a serious problem.

I think the current size is about 8 GB, not 40 GB, according to some recent posts (not running a node myself though).

You may be right, I'm just going by hearsay myself.

According to this it can handle more transactions per second: https://www.quora.com/How-scales-ethereum-in-comparison-to-b...

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