After only two weeks since its limited introduction, Google+ might already have at least 5-million users in the U.S.

A report in eWeek.com indicates that Paul Allen, the founder of Ancestry.com, came up with a figure of 4.7-million – up from 1.7-million on July 4. (His data does not include foreign users).

Other estimates are as high as 9-million users for the new social network site.

I updated about 1/4 of my surname counts tonight, and am very surprised at how fast the userbase is growing, Allen wrote on a blog on Google+ on his site.

Allen also wrote: “I have about 10x fewer followers on Google+ than [Kevin Rose, founder of Digg.com] does, but I have found a very engaging community there. If I post something there, I seem to get several times more interaction than anything I do on Twitter, Facebook, LinkedIn, or my blog. I don’t want to lose my 8 year archive of blog posts, but I’m not sure I’ll keep blogging on WordPress outside of Google+.”

Regardless, Google+ will have to keep growing at an astronomical pace to match Facebook, which has upwards of 750-million users worldwide.

eWeek estimates that if Google+ can grow by 5-million users per week for a whole year, it would still only have 250-million users (far short of Facebook’s number of users).