Export MS Access tables with random autonumber fields to MySQL

I am exporting a number of tables from MS Access to a new MYSQL
database. Many of the tables have random autonumber columns for their
primary key (they were prviously replicated). I would assume new records
in MYSQL will add "1" to the highest number in the indexed column. Will
this cause problems later when new records are added to MYSQL (ie
reaching the maximum value that could be stored in an integer field)?
Some of the tables have > 200,000 records- a sample highest value of the
Access autonumber column value would be 2147414576. Any suggestions?

Thanks,
G.L.