A bitcoin doesn't have a unique number at all. The unique number that you are thinking of is effectively an "account id". When bitcoins are mined, essentially a ledger gets created saying that "account id" #1234567343533 has 25.000000000 bitcoins in it. When you send someone money, you say "from #1234567343533, send 0.05000000 BTC to #111111111, and 24.95000000 BTC to #1234567343533"
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A bitcoin doesn't have a unique number at all. The unique number that you are thinking of is effectively an "account id". When bitcoins are mined, essentially a ledger gets created saying that "account id" #1234567343533 has 25.000000000 bitcoins in it. When you send someone money, you say "from #1234567343533, send 0.05000000 BTC to #111111111, and 24.95000000 BTC to #1234567343533"