screenshot by Stephen Shankland/CNET

Google+ appears to be in the midst of a population explosion.

A statistical analysis by Paul Allen, founder of Ancestry.com and chief executive of Facebook app maker FamilyLink.com, concludes that the Google+ population reached 7.3 million on Sunday, July 10, and likely will reach 10 million today.

And if Google keeps the Google+ invitation button active, as it has since Sunday, Allen expects Google+ to reach 20 million users by this weekend, he said in a Google+ post late Monday night.

"The user base is growing so quickly that it is challenging for me to keep up," Allen said.

A population of 10 million or 20 million is huge in absolute terms, especially given that the service is two weeks old today. But it pales to Facebook's 750 million, half of whom log in daily. Allen's statistics, though estimates, do provide evidence that there's demand for another sizable social network--and that Google isn't necessarily forever doomed to fail in trying to launch it.

Facebook and Google have been fierce competitors. Facebook more than any other company showed that new competitors could outdo Google in important online markets. Now, though, Google has shown that Facebook, too, can't take its incumbent power for granted.

Lutz Beyer/Cybay New Media

Google+ began with a small group of the tech in-crowd, but has been steadily expanding. The invitation button that let people add their friends had been a rarity, but the current explosion is doubtless fueled by the relatively easy availability of new invitations. In addition, it Google appears not to be throttling the sign-up rate, or is at least throttling it less, for those who receive invitations.

Allen isn't the only one impressed with the Google+ growth.

"I predict that Google+ will go from 0 to 100,000,000 users faster than any other service in history," said Bill Gross, founder and CEO of technology incubator Idealab, in a Google+ post yesterday. His reasons:

The service is great. It is timely. People are engaging with it like crazy. There are rumors that there are already 4.5m people. That might be high. It might be as low as 1m, or even lower, but my guess is that it's more than 1m people already. That already is probably the fastest growing service (0 to 1m) ever. Now it's not completely fair, since when Facebook started, and when Twitter started, etc. those were tiny companies, and Google is huge. However, the product is extremely well executed, and a lot of people are smitten. The next year will tell. Will there be bumps in the road? Sure. Will Facebook and Twitter fight back with more innovation? Of course! But I'm saying that Google+ is already good enough, and the team on Google+ is being so responsive in a way that makes me believe they have a real winner here.

To estimate Google+'s population, Allen tracks surnames that appear on the site. Here's how he describes his methodology:

My model is simple. I start with US Census Bureau data about surname popularity in the U.S., and compare it to the number of Google+ users with each surname. I split the U.S. users from the non-U.S. users. By using a sample of 100-200 surnames, I am able to accurately estimate the total percentage of the U.S. population that has signed up for Google+. Then I use that number and a calculated ratio of U.S. to non-U.S. users to generate my worldwide estimates. My ratio is 1 US user for every 2.12 non-U.S. users. That ratio was calculated on July 4th through a laborious effort, and I haven't updated it since. That is definitely a weakness in my model that I hope to address soon. The ratio will likely change over time.

He's working on updates to his approach, too. At some point, though, it'll likely be made obsolete by Google itself, when the company concludes the time is right to trumpet its success.