Miami ? Bill became a major hurricane far out in the Atlantic on Tuesday, with winds whipping near 125 mph, and forecasters say it could strengthen even further.

The National Hurricane Center said people in the Leeward Islands should monitor Bill’s progress, though the core of the dangerous storm was expected to pass well northwest of the islands late today and early Thursday.

Hurricane hunter planes found that Bill, the first hurricane of the Atlantic season, had strengthened to a Category 3 storm Tuesday night.

“The wind sheer is light and the waters are warm,” said Todd Kimberlain, a forecaster at the center. “Those are two essential ingredients not just for the formation, but also the maintenance, of hurricanes.”

Bill was centered about 555 miles east of the Leeward Islands, moving west-northwest near 15 mph.

The most significant threat could be to Bermuda, which the storm could pass in three or four days, Kimberlain said.