The private key (comparable to an ATM PIN) is meant to be a guarded secret, and only used to authorize Bitcoin transmissions. Thus, it’s the “private key” that is kept in a Bitcoin wallet. Some safeguards for a Bitcoin wallet include: encrypting the wallet with a strong password and choosing the cold storage option, i.e. storing it offline. In the case of Coinbase, they offer a secure "multisig vault" to host your keys, which you can sign up for. 
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The bank transfer can take up to 3-4 business days to reach the bank account. Once it is received, your exchange will be processed and the bitcoins will be transferred to your bitcoin wallet. Due to the awesome world of bitcoin, the bitcoins will be transferred to your wallet instantly and after 3-6 confirmations, depending on your choice of wallet, you will be able to spend your bitcoins to buy goods online.
The receiver of the first bitcoin transaction was cypherpunk Hal Finney, who created the first reusable proof-of-work system (RPOW) in 2004.[22] Finney downloaded the bitcoin software on its release date, and on 12 January 2009 received ten bitcoins from Nakamoto.[23][24] Other early cypherpunk supporters were creators of bitcoin predecessors: Wei Dai, creator of b-money, and Nick Szabo, creator of bit gold.[25] In 2010, the first known commercial transaction using bitcoin occurred when programmer Laszlo Hanyecz bought two Papa John's pizzas for 10,000 bitcoin.[26]
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