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I had installed bitcoin-wallet app on an old phone a couple of years ago, just out of curiosity about bitcoin. I obtained somehow a teeny amount of bitcoin, .0017xxxx anyway, I installed the app on a new phone, and exported/imported. This all worked fine.

I am just curious about what then happened... on the new one after the import, it initially said something to the effect of "recreating (resyncing?) 30 months of history" or something. And very very slowly the number of months went down and eventually got done, taking maybe a day. I did notice the phone was pretty warm :-) Afterward, I had to chuckle because I just happened to notice the phone said it had used 50GB of data that day (!)

Is that all normal? What was it doing all that time? Is it necessary?

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Most mobile wallets are light-clients, meaning they don't download and validate the entire blockchain history. Instead, they just download the block headers (80 bytes per block), and then request any additionally needed block/transaction data that is related to the addresses that the wallet controls.

At the time of writing, the network is currently at blockheight ~623,000, so we should expect a light client to download about this much data:

623000 blocks * (80 bytes / block) = 49,840,000 bytes = ~50 Mb

The actual amount will likely be slightly higher, but we can get an idea for the order of magnitude of data from this estimate.

So, assuming that this wallet is just a light-client, it is odd that it would download 50 Gb of data. If this is the app you are mentioning, the recent user reviews make it sound like this excessive data usage is a bug (see the dev responses on that page).

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