According to independent analysis done by Paul Allen, founder of Ancestry.com, Google's new social network Google Plus will hit 20 million users by this weekend. And he estimates that the current user base has already surpassed the 10 million mark.

What's most surprising about Google Plus, however, is how quickly it has grown. The size of the user base has increased by 350% in just 6 days, says Allen.

The Google Plus Membership Model

To determine these figures, Allen used surname-based analysis, a tactic he's quite familiar with from the years he spent at Ancestry.com. His model uses U.S. Census Bureau data about surname popularity in the U.S. and compares it to the number of Google Plus users with each surname. He also split the U.S. users from the non-U.S. users in his analysis, since Google Plus is open in international markets, too.

Allen used a sample of 100 to 200 surnames to estimate the total percentage of the U.S. population who has signed up for Google Plus. He then used that number and a calculated ratio of U.S. to non-U.S. users (one U.S. user for every 2.12 non-U.S. users) to generate his worldwide estimates.

Because he's been tracking surnames since his first day on the site, he has been able to accurately measure growth. Although these figures are still unverified and unconfirmed by Google, Allen says his model is sound. Earlier estimates based on this model pegged the user counts at 1.7 million on July 4th and 4.5 million on July 9th.

Great Growth, but Not a Facebook Threat Yet

Allen also reports that his current company FamilyLink, makers of several Facebook applications, is set to reveal survey data involving Facebook users' knowledge of and reaction to Google Plus sometime this morning.

"Facebook investors and employees will be very happy to see that the vast majority of their active users are happy at Facebook, and most of them haven't even heard of Google+ yet," writes Allen. "So even though Google's growth is staggering, there is a huge loyal Facebook following who may not see a need to switch," he says.

Google Plus's estimated 20 million also pales in comparison to Facebook's 750 million, half of which still log on to Facebook any given day. Google Plus, meanwhile, is seeing a lot of engagement too, but it's still the new shiny toy of the Internet digerati, who often glom onto and obsess over the latest hip service until an even hipper one comes around.

But Google knows it needs to make Google Plus a regular habit once the new car smell wears off. According to Mark Striebeck, Google's Engineering Manager for Gmail, the company is planning to integrate the service into Gmail (and wants your ideas for that).  While Google's previous attempt at merging social with Gmail (i.e. Google Buzz) was essentially a failure, Gmail could still serve as a large built-in user base for the emerging social network, assuming the integrations are thoughtful, useful and capable of enhancing the core Gmail offering itself.

Current estimates put the Gmail user base at around 200 million. Although not all Gmail users will join Google Plus, it's a large, captive market for Google to get its hooks in. And yet, even if all 200 million Gmailers joined Google Plus, it would not even be half the size, or a third of the size of Facebook. It's no wonder why Google's strategy is to be just "another" social networking service, instead of a "Facebook killer."