Analysts are predicting that Apple will quickly ramp up production of the Apple Watch, now that preorders of the device appear to have rapidly outpaced supply.  Although the watch does not even go on sale until April 24, according to the report in Reuters, Apple’s website now lists shipping times for the new device anywhere from four to six weeks, to as late as June for some models.

“Overall we view the trends over the weekend as an indication of solid demand paired with very limited supply, with supply being the most significant limiting factor,” Piper Jaffray Financial analyst Gene Munster said in a client note, according to Reuters.

Munster expects Apple to sell roughly 2.3 million watches during the April-June quarter, precipitating a ramp up in production around mid-May through June. And those numbers could be on the conservative side.

Other market analysts predict even stronger sales, Reuters reports. BofA Merrill Lynch predicts that Apple will ship 4 million smartwatches in the April-June quarter, while Cowen predicts 3 million. Meanwhile, UBS speculates that Apple could sell 16 million watches by September, and a total of 40 million in fiscal year 2016.

Analysts at Pacific Crest told Reuters that Apple appeared to be ordering enough components to build 20 million Apple Watches this year, providing more evidence of an imminent production ramp up.

Only about 720,000 Android-powered smartwatches were shipped in all of 2014.