A production number attached to a scene heading so every department refers to the same unit — Scene 42 stays Scene 42 after a lock, even if pages shift.
Spec scripts usually omit scene numbers. Shooting scripts add them when the draft becomes a production document that departments must cite in boards and sides. Scene 42 should mean the same unit for wardrobe, locations, and the AD even after nearby pages gain revisions overnight.
After lock, omitted or inserted scenes get lettered numbers such as 42A rather than renumbering the entire show. Renumbering would break sides, lined scripts, and schedules that already point at the old digits. Letter suffixes preserve history while new units appear in the continuum.
Writers sometimes number a spec to look "more professional." Readers often read that as a shooting-draft costume on a sales draft. Add numbers when production, a classroom assignment, or a specific submission guideline asks for them -- not as decorative seriousness on the first page.
Generally no -- readers treat numbered specs as trying to look like shooting drafts. Add numbers when production or a classroom assignment asks for them.
It usually marks a scene inserted after lock without renumbering the whole script. Scene 12 stays 12; the new unit between 12 and 13 becomes 12A so schedules do not break.
Typically the production office or AD team issues numbered drafts. Writers should not freestyle renumber mid-prep once sides and boards already depend on the published scheme.
In shooting scripts they sit with the scene heading as the shared reference. In specs, leave them off and let the heading's location and time do the orientation work alone.