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Parity UI displays current block number at the bottom, but if UI is not enabled, then how do we find the current block number?

Is there a way to find current block number

using JSONRPC ?
Is it stored somewhere in basepath?
Note: If anyone can find proper tags, please update it! Currently there is no tag for parity.

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To get the latest block number over RPC, you can call the 'eth_blockNumber' method. 

See this from the https://github.com/ethereum/wiki/wiki/JSON-RPC#eth_blocknumber: 

// Request

curl -X POST --data '{"jsonrpc":"2.0","method":"eth_blockNumber","params":[],"id":83}'

// Result

{

  "id":83,

  "jsonrpc": "2.0",

  "result": "0x4b7" // 1207

}

Also, there are other higher-level APIs like web3.js or web3.py. These allow users to use web3.eth.blockNumber to get the latest block number. These APIs generally work in native types rather than hex strings.

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