primogeniture
Concise Oxford English Dictionary © 2008 Oxford University Press:
primogeniture /ˌprʌɪmə(ʊ)ˈdʒɛnɪtʃə/
▶noun the state of being the firstborn child.
■ a rule or tradition of inheritance by the firstborn child.
– derivatives
primogenital adjective,
primogenitary adjective.
primogenital adjective,
primogenitary adjective.
– origin C17: from med. L. primogenitura, from L. primo ‘first’ + genitura ‘geniture’.
'primogeniture' also found in these Oxford entries:

