modern way to write dates

How to say dates in the modern way, written like here:
?
Is today's date (23 January 2020) would be pronounced "diē vīcēsimō tertiō mēnsis iānuāriī annō bis mīllēsimō vīcēsimō"?
 
Yes, I know that Romans used their own system:
,
but I didn't write the date in the video that way. Someone with way more knowledge of Latin than me did.
 
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