primogeniture (n.)

"right of succession of the first-born, descent to the eldest son," c. 1600, from French primogeniture and directly from Medieval Latin primogenitura, from Late Latin primogenitus "first-born," from Latin primo (adv.) "first in order of time," from primus "first" (see prime (adj.)) + genitus, past participle of gignere "to beget" (from PIE root *gene- "give birth, beget"). Earlier in English it meant simply "fact or state of being first-born among children of the same parents" (1590s).