What does decem prīmī mean in Latin?

decem prīmī, a noun, means “the heads or presidents of the ten decuriae which usually formed the senate in an Italian city or Roman colony.”.

What is the genitive of decem prīmī?

The genitive singular is decem prīmōrum. decem prīmī is second declension.

In classical Latin, [ˈdɛ.kẽː ˈpriː.miː]; in ecclesiastical (church) Latin, [ˈdɛː.t͡ʃem ˈpriː.mi].

nounsecond declension

decem prīmī m pl (genitive decem prīmōrum)

Classical[ˈdɛ.kẽː ˈpriː.miː]Ecclesiastical[ˈdɛː.t͡ʃem ˈpriː.mi]

the heads or presidents of the ten decuriae which usually formed the senate in an Italian city or Roman colony.
evocat ad se Centuripinorum magistratus ei decem primoshe summons before him the magistrates of Centuripa and the ten principal citizens.70 BCE, Cicero, In Verrem 2.2.162
Itaque decurionum decretum statim fit, ut decem primi proficiscantur ad L. Sullam doceantque eum, qui vir Sex. Roscius fuerit...Therefore a decree of their senate is immediately passed, that the ten chief men should go to Lucius Sulla, and explain to him what a man Sextus Roscius had been;80 BCE, Cicero, Pro Roscio Amerino 25

From decem (“ten”) + prīmus (“first”).