Serial Foreign Key

Suppose I have two tables:

create table t1 (
   id    serial    not null
);

create table t2 (
   id    serial    not null,
   t1    integer    not null,
   foreign key (t1) references t1 (id)
);

Should the "t1 integer" actually be a bigint?  I ask because when I do
"select * from t1_id_serial" the max_value is much larger than 2^32.
Does this vary from system to system?

Thanks,
jonathan