Now that the first weekend during which the iPad 2 was available is over, sales estimates are coming in left and right, and they tend to be quite positive.  Piper Jaffray, for example, believes that perhaps 500,000 iPad 2s flew off shelves, and Wedbush Securities thinks a number in the neighborhood of 1 million is possible.

To start with the less optimistic guess: Philip Elmer-DeWitt, who got a look at the Piper Jaffray report, wrote, “[Senior Research Analyst Gene] Munster is sticking with his estimate of 400,000 to 500,000 iPad 2s sold, compared with 300,000 iPad 1s in its first weekend last year.”

Then DeWitt continued, “The difference is that nearly all those iPad 2s were sold in one day; stocks were essentially depleted by Saturday and not replenished.  In its calls to retailers over the weekend, his team was unable to find a single iPad 2.”

Piper Jaffray contacted retailers in New York and Minneapolis, by the way, and we can confirm that Target stores in Lexington, Kentucky ran out, as well.

As for Wedbush Securities, analyst Scott Sutherland told Reuters, “We would not be surprised to see Apple sell closer to 1 million iPad 2s in the opening weekend.”

Either way, that’s quite impressive.  Most people are willing to admit that the iPad 2 doesn’t represent a huge leap forward compared to the original iPad, and the price didn’t come down at all, so it looks like demand for Apple-branded tablets is just rising on its own.

That appears to have pushed Apple’s stock up this morning (0.06 percent), even as the Dow and Nasdaq are already way down (1.08 percent and 1.18 percent, respectively).