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I am trying to run a full node on rinkeby network using command

geth --rinkeby

but , I cannot figure out why the processed block size [2382419] is greater than the current block height which was [1624447] while writing this post on https://rinkeby.etherscan.io/blocks

I have attached a screen shot enter image description here

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I think you're incorrectly comparing the block size with the block number.

The block size is just how big that specific block is (in bytes). It's found in your output next to bytes=. The block number starts at 0 for the genesis block that started the whole chain, and then it goes up in sequence. The "block height" is just the highest available block number.

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Maybe not your questions but note there's 2 different types of Rows in the image you've posted. One is regarding state entires under Imported new state entries and the other is regarding block receipts under Imported new block receipts. State entries and block receipts are different things.

The state entries are the nodes in a tree data structure that holds the current state of all the contracts and accounts. The processed field in the state entries row refers to how many nodes in that tree have been downloaded.

The block receipts are details of each block which are necessary to validate the blockchain. The number in the block receipts row refers to the most recent block your node has downloaded.

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