Early this morning on his Google+ account, Ancestry.com founder and entrepreneur Paul Allen wrote a lengthy post about user estimates on the brand new social network. His estimates show that the rate of growth of Google+ is not only strong, but staggering.

Allen suggested on Sunday that there were probably close to 5 million users currently on Google Plus. They way he calculated this figure is based on U.S. Census Data of specific surnames compared to registered users on Google+.

In his post this morning he explains his process further -

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.

Using that model, Allen has predicted that sometime today, Google+ will top 10 million users. This is based on the fact that the tally reached 7.3 million users yesterday, which signifies a 350% increase in six days. At the time of his post, he estimated 9.5 million users. That means over 2 million joined Google+ in roughly a day and a half.

If Allen’s estimates are accurate, then it is likely that Google+ has already broken through the 10 million user mark as you read this.

“I’m not claiming perfect accuracy,” he says. “But I do think the model is sound.”

He also thinks that Google+ could hit 20 million users by this weekend. Of course this is contingent on the Invite Button remaining available – which right now it is. After a period of on and off availability of invites, Google is currently allowing new users into the social network, and has been for a couple of days now.

As the membership continues to grow, maybe the gender distribution will even itself out. As of right now, males outnumber females registered to Google+ by an astounding margin.

With this kind of growth, it doesn’t seem out of the question that Bill Gross is right, and Google+ will be the fastest social network to reach 100 million users.