Importing contacts for existing/imported customers

Importing contacts for existing/imported customers

What is the format for the customer-ID to link contacts to companies successfully?
I have tried a dozen times but have never been successful.
Does the import csv for the contacts need to use a special format for the customer IDs?
In my case the typical customer IDs (when displayed in the sheet view) are like:
'1399931000000084007
Using the same IDs importing the contacts did not link the contacts though...
THX for a feedback