Google+, the newest social networking stream on the planet, could go on to boast 20 million users by the weekend, according to Paul Allen, the founder of and a serial entrepreneur.

Allen wrote in his Google+ wall that the social media platform may reach the 20 million users mark by this weekend. Allen did a summary analysis on the Google+ user base and said that the social networking stream has been successful in surpassing the 10-million mark.

Allen estimated that Google+'s population had reached around 7.3 million on Sunday and would hit the 10 million milestone at some point Tuesday.

Allen made use of a combination of surnames and population data from the U.S. Census Bureau and made a rough estimate about the number of users in Google+. He later split the U.S. users from the non-U.S. users by using a sample of 100-200 surnames. The growth numbers assume that Google won't restrict users from inviting their friends this week, as it did in the last week.

“My surname-based analysis shows that the number of Google+ users worldwide reached 7.3 million Sunday (July 10) – up from 1.7 million users on July 4th,” Allen wrote in his Google+ wall. ”That is a 350 percent increase in six days. The user-base is growing so quickly that it is challenging for me to keep up, since the number of users of any given surname (even the rare ones I am tracking) seems to be climbing every day.”

Even if Allen's estimate proved accurate, the numbers still pale when compared to the estimated 750 million users currently logging onto Facebook.

Despite this, Allen went on to reiterate his belief that Google+ may yet turn into a valid competitor for Facebook, arguing that there is statistical evidence to suggest a large enough demand to keep the service afloat.

Meanwhile, Google has admitted that it has run out of disk space for its Google+ social networking service according to its SVP of social networking, Vic Gundotra.

Gundotra wrote on his Google+ profile, For about 80 minutes we ran out of disk space on the service that keeps track of notifications. Hence our system continued to try sending notifications. Over, and over again. Yikes.

He added that Google didn't anticipate the service to hit a high threshold so quickly but that the company should have.

Gundotra's comment also said that there will be more changes to the social network service this week to address some criticisms. Google+ users should hope that means more disk space.