Primary skills are the skills that a guild or guild specialisation teaches up to level 300. They are generally the skills that exemplify the philosophy or attributes of that guild/specialisation, and feature prominently in many of the abilities available to that guild.
All primary skills can be learned from guild teachers. They will levy a small charge for this service, which increases based on the level learned.
Learning a level in a primary skill from one's guild is cheaper than learning it from anywhere else.
Advancement XP cost
The following formula gives the XP cost to advance one level in a primary skill by learning from one's guild:
<cost> = RoundDown( 75 * RoundDown( <previous_level>/3 + 1 ) * exp(<previous_level>/150))
Advancement monetary cost
The following formula gives the monetary cost to advance one level in a primary skill by learning from one's guild, in Ankh-Morpork dollars:
<cost> = RoundDown(<xp-cost> / 80 ) / 100
A player's guild level is the rounded down average of their level in all their primary skills.