primogeniture

noun

the right, by law or custom, of the paternally acknowledged firstborn son to inherit his parent's entire or main estate, in preference to daughters, elder illegitimate sons, younger sons and collateral relatives

Pronunciation: /ˌprʌɪmə(ʊ)ˈdʒɛnɪtʃə/

Etymology: From French, from Late Latin primogenitura, from Latin primus (“first”) + genitura (“birth”) (from genitus, past participle of gignere).

The state of being the firstborn of the children of the same parents.
The principle that the eldest child has an exclusive right of inheritance.
“On these grounds, I contend the mere possession of large property, which is all that primogeniture insures, is by no means a sufficient and unobjectionable qualification for a legislator.”
“Anglo-Saxon kings did not succeed on the basis of primogeniture. All the kings offspring were known as aethelings -- throneworthy -- and from this gene pool the royal family would select the aetheling who seemed best qualified for the job.”
An instance of such a right of inheritance, established by custom or law.
“The King of Sardinia, by a decree of the 9th of Dec. has abolished— 1. The prohibition against the erection of primogenitures and feudal rights, enacted by the 9th section of the edict of the 29th of July 1797, or by any other law; restricting, however, to those primogenitures and majorats only which shall be erected in favour of persons[…].”
“All primogenitures, trusts, rights of presentation, and every other description of entail on real property, movables, or fixtures, rents, annuities, seigneuries, or of any other kind whatsoever, are suppressed, which are from henceforward restored to the class of absolutely free.”