Because Amazon doesn't release its Prime membership numbers, third-party researchers such as Cowen & Co make estimates based on polling. Their latest research - based on a sampling of 2,500 U.S. consumers - found that membership had risen by 23 percent year-over-year (y-o-y).

Cowen & Co found that 83 percent of Prime members purchased from Amazon in October, as opposed to 49 percent of U.S. consumers without membership.

The numbers were also good news for Amazon's grocery delivery products with the number of "Grocery and consumable" purchases at Amazon up 12 percent y-o-y. The report spelled bad news for the competition. Wal-Mart, which ratcheted up the competition with Amazon through its $3.3bn purchase of Jet.com in August, saw the same in-kind purchases fall 2 percent. Target did only marginally better, with purchases up 1 percent.

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