The CRN system can best be understood as a regional registration system. Your design needs to be registered in each jurisdiction (province or territory) where it will be used.
CRNs take various forms - 5AN0123.5, 357.1, M0123.2, OH9999.3 could all be legitimate CRNs registered in one jurisdiction only - the number after the decimal point. For example AN0123.5 is registered in Ontario (5).
A design can be registered in more than one jurisdiction - ie 357.12 - a design first registered in B.C. and then in Alberta. The first digit after the decimal is important. 357.21 would be a different vessel first registered in Alberta, then in B.C. A design can be registered in all the jurisdictions which would look like this - 357.2134567890NYT and can be shortened to 357.2C. The first jurisdiction of registration is always shown (2 or Alberta in this case). The C indicates that every jurisdiction has been registered.
Note: piping registration numbers do not always indicate which province they are registered in: P30337 is a piping system registered in Ontario.