I presume you mean the serial/registration numbers most organizations put on their black belt certificates. Organizations use different numbering systems but all the systems serve the same purpose.
Since each number is unique and is issued and stored by the organization, it helps identify the person, and it helps prevent forgeries. Since the numbers are consecutive, they indicate the person's seniority in the organization, and they indicate the number of certificates that rank that have been issued by the organization. Sometimes letters are used in the number to indicate the rank of the certificate.
Registration numbers are not required, but they are used by all major organization to help prevent a phony black belt from making a copy of a real certificate and putting his or her name on it. When in doubt about a black belt's certification, you may check with the issuing organization; the organization can use the registration number to verify if the person is a legitimate black belt.
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