What is the maximum length (if string) or size (if number) of a serial number?

I am using the current datetime to set the initial serial number for my CA to provide a reasonable measure of uniqueness:

 # example: 200507171152001
 SERIALINIT=$(date +%Y%m%d%H%M)001
 echo $SERIALINIT > serial

Do I need to be concerned with the number of characters or the number of bits used to represent the serial number? Is there an RFC that defines this?

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