Google+ has an estimated 10 million users

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Google+ may still be in invite-only testing mode. But that hasn’t stopped the new social network from amassing an estimated 10 million users in the two weeks since the site went live. That number comes via founder Paul Allen, who estimates that Plus “could reach 20 million users by this coming weekend,” if Google continues to allow new people to join.

According to Allen, “the number of Google+ users worldwide reached 7.3 million [on July 10] – up from 1.7 million users on July 4th. That is a 350% increase in six days.”

Allen based his estimate by first looking at the number of people in the United States with each surname, according US Census figures. The total number of people with a certain surname was then compared to the number of US-based Google+ users with that surname. (Allen used a sample of 100 randomly selected surnames for the test.) The ratio Allen came up with “though a laborious effort” is “1 US user for every 2.12 non-US users.” And it is through this ratio that he came up with his total Google+ user numbers.

Allen admits that the ratio he came up with is the primary “weakness” in his model, but says that he hopes to update the ratio soon.

“I am not claiming perfect accuracy, but I do think the model is sound,” writes Allen. “A quant has suggested a mathematical formula that I can use to calculate a range of Google users with a 99% level of accuracy, and one of my employees is working on that math now. I hope to include that in future models.”

Google has not yet released any specific user numbers for Google+. That said, the company’s executive chairman, Eric Schmidt, admitted during an interview on Saturday that the number was in the “millions,” which adds to the possibility that Allen’s estimates are correct, or at least in the right ball park.

For comparison: Twitter currently has more than 200 million users; Facebook has more than 750 million.

Check out all our Google Plus coverage here.