Bash / shell
You may exclude from the 10-character limit any code necessary to print anything.
... you can use up to 16 characters for your program.
(6 chars for code + 7 chars for printing = 26 digits) = 6888888 digits
$ seq -s9 999999
This number is bigger, but people may argue that it's in the wrong format.
The output may be in any format (so you can print 999, 5e+100, etc.).
(8 chars for code + 8 chars for printing = 26 digits) = more than 1183888008 digits
$ seq -s9 99999999
It usually takes around a minute to print the number and it contains the scientific representation of it.
Some funny example:
(10 chars = 26 digits)
echo $$$$$$$$$$
2760127601276012760127601
See: What does $$ mean in the shell?What does $$ mean in the shell?