Primary statistics are numerical representations of characters' inherent abilities. In the SPECIAL character system, there are 7 Primary Stats. Their first letters form the name of the system itself.
The primary statistics form the base for all derived statistics.
For humans, Primary Statistics cannot go below 1 or above 10 during creation. For other races (available only in Fallout Tactics), Primary Stats can go as high as 16. Each race or species has different minimum and maximum stat requirements. In Fallout and Fallout 2, the Primary Statistics cannot go below 1 or above 10 even with bonuses in game. In Fallout Tactics, bonuses from items can increase the statistics beyond their natural racial maximum.
In Fallout 3, the S.P.E.C.I.A.L system minimum is 1 and the maximum is 10, but it can be raised "invisibly". For example, if the player has 10 Agility and then finds the Agility Bobblehead, Agility is still represented as 10 in the Pip-boy stats page, but if there ever is a negative modifier--for example, Metal Armor (Ag -1)-- the Agility stat will still show 10, because the player's Agility is technically 11 in this case, this can be confirmed on the PC version of the game using the command
In Fallout Tactics, each race has some points distributed already at character creation. It does not, however, really matter, as they can be subtracted and added to anyway. Generally, humans have 40 points to distribute among their characteristics. The numbers for other races are 42 for ghouls, 40 for super mutants, 41 for deathclaws, 45 for humanoid robots, and only 35 for dogs. Races with more than 40 character points generally have slower Perk Rate.