tall = the generic word for (cardinal) numbers
siffer = digit, not the kind you have on your hands
antall = number of something; quantity of countable noun
mengde = amount of something; quantity of uncountable noun, ++
nummer = used for a number in an order, and for identification numbers, phone numbers, etc.
ordenstall = ordinal number with ordinal ending
"Hva er yndlingstallet ditt?"
"Tallet hadde fem siffer."
"Et firesifret tall"
"Et stort antall studenter"
"Antallet må økes."
"Nedbørsmengden er stabil."
"Han er nummer fire."
"Husnummeret vårt er 86."
"Vi trenger ditt fødselsnummer."
"Hun kom på fjerdeplass."
"Fjerde er et ordenstall."
I am not 100% certain, but I think of "å kjenne" as "to be familiar with", and that is why it applies to personal things like people. Whereas "å vite" is "to know (a fact)" and would apply to whether you knew a fact or not.
In this sense, perhaps the sense could be translated as "I am not familiar with the number.", or "I do not (personally) know that number.", perhaps in reference to an unknown telephone number.