pri·mo·gen·i·ture 
(prī′mō-jĕnĭ-chr′)
(prī′mō-jĕnĭ-chr′)n.
1. The state of being the firstborn or eldest child of the same parents.
2. Law The right of the eldest child, especially the eldest son, to inherit the entire estate of one or both parents.
[Late Latin prīmōgenitūra : Latin prīmō, at first (from prīmus, first; see per1 in the Appendix of Indo-European roots) + Latin genitūra, birth (from genitus, past participle of gignere, to beget; see genə- in the Appendix of Indo-European roots).]
pri′mo·geni·tar′y (-jĕnĭ-tĕr′ē), pri′mo·geni·tal (-təl) adj.