Which pool has the highest streak of finding a lot blocks in a row?
depends if you mean an honest streak (using unmodified stratum/bitcoind code), or how antpool as well as f2pool/others actually manage to do it.
they basically find a block, dont announce it, continue mining on the new block, rinse and repeat. well known practice.
easily spotted with either no or very few transactions.
good example is:
https://blockchain.info/rawblock/00000000000000000472036667817f445167d11c44f998fff31c674fc4043111
another 'trick' is to run what is known as a 'dead miner' on a bunch of different pools. it is essentially cgminer/bfgminer running on a stratum pool with no ASIC connected. this allows any new block hash to be retrieved far quicker than waiting for a full block to be received by your local bitcoin daemon.
once you have the latest block hash, slap it through libblktemplate and hand it to your stratum.
both methods revolve around getting a head start against the other pools.
which block numbers specifically?