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I have a few questions regarding light clients (such as Electrum and Multibit).

  1. Are they connecting to full nodes directly (using port 8333) or to another kind of server on another port?

  2. If they do not connect to the bitcoin network directly (on port 8333), why is that? Why is it necessary to be a full node (with the whole blockchain) to communicate in the bitcoin network?

  3. In the case of Electrum, it seems to connect to an Electrum server, which runs a full node. What are the advantages of doing so instead of connecting directly to the bitcoin network on port 8333 (assuming that it would be possible)?

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  1. Are they connecting to full nodes directly (using port 8333) or to another kind of server on another port?

Electrum no, Multibit yes.

  1. In the case of Electrum, it seems to connect to an Electrum server, which runs a full node. What are the advantages of doing so instead of connecting directly to the bitcoin network on port 8333 (assuming that it would be possible)?

It is a different trade-off. Electrum relies on other servers to index the addresses used in the chain, and queries them. Multibit (and other so-called "SPV clients") ask full nodes to scan the chain for them, but as normal full nodes don't have (or need) a full index of all used addresses, this isn't as efficient.

There is also a privacy trade-off. Electrum's privacy relies on the Electrum servers not being compromised (you can run your own, but few users do). Multibit's privacy relies on the BIP37 bloom filter mechanism for letting full nodes scan the chain for them. This method has been shown to be significantly flawed however, and the (randomly selected) nodes it queries transactions from could easily learn a lot about the wallet.

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