Primero vs. primer
The Spanish words 'primero' and 'primer' both translate to 'first' in English. They are both used to indicate the initial item in a series, but their usage depends on the gender and number of the noun they modify.
Primero
'Primero' can be used to denote 'first' in a general context, or when referring to masculine singular nouns. However, it is primarily used with masculine plural nouns or when no noun follows.
Vivo en el primero piso.
(I live on the first floor.)
De los tres hermanos, él es el primero.
(Of the three brothers, he is the first.)
Primero vamos a la tienda y luego al cine.
(First we go to the store and then to the movies.)
Primer
'Primer' is an apocopated form of 'primero', used immediately before a singular masculine noun. It does not apply to neuter or non-gender specific nouns in Spanish.
Es el primer día del mes.
(It is the first day of the month.)
Este es mi primer carro.
(This is my first car.)
Es la primer manzana que como hoy.
(This is the first apple I eat today.)
Summary
'Primero' and 'primer' both mean 'first', but their usage in Spanish varies based on the gender and plurality of the noun they modify. Specifically, 'primer' is used before singular masculine nouns, whereas 'primero' is more generally used, including with plural masculine nouns or when no noun follows.