It is a specific number that is registered to an individual for identification use.
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the ID number on your ID card
That is your trainer's ID number.
The ID number is 383
The ID number is the original trainer's ID, the person who caught or hatched the Pokémon.
The ID number of any Pokemon is given to it by the trainer - namely, you. Your ID number is given to every Pokemon you own. So, no specific Pokemon has any specific ID number. It is the trainer that gives the Pokemon the unique ID number.