Satoshi predicted and had no problem with a few large mining farms vs the majority of users being miners

The current system where every user is a network node is not the intended configuration for large scale.  That would be like every Usenet user runs their own NNTP server.  The design supports letting users just be users.  The more burden it is to run a node, the fewer nodes there will be.  Those few nodes will be big server farms.  The rest will be client nodes that only do transactions and don't generate.
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The design outlines a lightweight client that does not need the full block chain.  In the design PDF it's called Simplified Payment Verification.  The lightweight client can send and receive transactions, it just can't generate blocks.  It does not need to trust a node to verify payments, it can still verify them itself.

The lightweight client is not implemented yet, but the plan is to implement it when it's needed.  For now, everyone just runs a full network node.

I anticipate there will never be more than 100K nodes, probably less.  It will reach an equilibrium where it's not worth it for more nodes to join in.  The rest will be lightweight clients, which could be millions.

At equilibrium size, many nodes will be server farms with one or two network nodes that feed the rest of the farm over a LAN.

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Simplified Payment Verification is for lightweight client-only users who only do transactions and don't generate and don't participate in the node network.  They wouldn't need to download blocks, just the hash chain, which is currently about 2MB and very quick to verify (less than a second to verify the whole chain).  If the network becomes very large, like over 100,000 nodes, this is what we'll use to allow common users to do transactions without being full blown nodes.  At that stage, most users should start running client-only software and only the specialist server farms keep running full network nodes, kind of like how the usenet network has consolidated.
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