Of the 12 rules only the first 6 have to be satisfied for a database to be called “relational” but there is a rule 0 which has to be obeyed - perhaps they should be called Codd’s 13 rules?
Rule 0: Relational Database Management
For any system that is advertised as, or claimed to be, a relational database management system that system must be able to manage database entirely through its relational capabilities.
Rule 1: Representation of information
All information in a relational database is represented explicitly at the logical level and in exactly one way - by values in tables.
Rule 2: Guaranteed logical accessibility
Each and every datum in a relational database is guaranteed to be logically accessible by resorting to a combination of table name, primary key value and column name.
Rule 3: Systematic representation of missing information
Null values (distinct from the empty character string or a string of blank characters and distinct from zero or any other number) are supported in fully relational database management systems for representing missing information and inapplicable information in a systematic way, independent of the data type.
Rule 4: Dynamic online catalog
The database description is represented at the local level in the same way as ordinary data, so that authorized users can apply the same relational language to its interrogation as they apply to the regular data.
Rule 5: Comprehensive data sub-language
A relation system may support several languages and various modes of terminal use (for example, the “fill in the blanks mode”). There must be, however, at least one language whose statements are expressible, per some well defined syntax, as character strings, and that is comprehensive in supporting all of the following items:
Transaction boundaries (begin, commit, rollback)
Rule 6: Updatable views
All views that are theoretically updatable are also updatable by the system.
Rule 7: High level insert, update and delete
The capability of handling a base relation or a derived relation as a single operand applies not only to the retrieval of data, but also to the insertion, update and the deletion of data.
Rule 8: Physical data independence
Application programs and terminal activities remain logically unimpaired whenever any changes are made in either storage representations or access methods.
Rule 9: Logical data independence
Application program and terminal activities remain logically unimpaired when information-preserving changes of any kind that theoretically permit unimpairment are made to the base tables.
Rule 10: Integrity independence
Integrity constraints specific to a particular database must be definable in the relational data sub language and storage in the catalog, not in the applications program.
Rule 11: Distributed independence
Whether or not a system supports database distribution, it must have a data sublanguage that can support distributed database without impairing application programs or terminal activities.
Rule 12: The nonsubversion rule
If a relational system has a low-level (single-record-at-a-time) language, that low-level cannot be used to subvert or bypass the integrity rules and constraints expressed in the higher level relational language (multiple-records-at-a-time)
Testing to see if a number is a prime or not is the basis of many encryption and security methods. It has long been assumed that there is no fast way, i.e no polynomial time method, to determine if a [ ... ]