Google+, the social networking product from the search engine giant, is heading for 20m users within the next few days just three weeks after its launch, according to calculations.

Paul Allen, the founder of Ancestry.com, said on Wednesday that his model which calculates its growth by the prevalence of surnames, indicates that by last Monday the site had hit 18m users and was growing at 750,000 per day.

The Google+ app for the iPhone, which was released earlier in the week, was the top free app on Apple's iTunes Store.

Allen said that the rate of growth has slowed slightly since last week, when there were a million people joining per day.

Google+, which is built as a social network that uses the idea of "Circles" - user-generated groups of people with whom to communicate. The idea is, like Twitter, to allow a wider social group than can be created on Facebook, without the need for reciprocity that its "friends" system requires, while letting people post at length rather than Twitter's 140-character limit.

Allen says that the potential for growth is enormous: "Google hasn't started marketing Google+ through any of its other channels yet. More than a billion people worldwide use Google products, including its top rated search engine, YouTube, and Blogger. Chairman Eric Schmidt says the vision is to integrate Circles and sharing with all the other Google properties. When that happens, you will likely see millions of people joining Google+ every day for some period of time."

Larry Page, the chief executive of Google, expressed delight with the growth of the service following the company's record profits and revenues last week. At the time he said that Google+ had passed 10m users. Allen says that his own model at the time showed 13m users, indicating that it is probably broadly accurate.

Allen explains his methods: "I don't have access to log files or to a massive consumer panel. I'm simply measuring how many Google+ users there are of various randomly selected surnames every day. Last week I increased the sample of surnames that I query from 100 to 1,000.

"Over a four-day period, the 100-surname sample showed a Google+ growth rate of 28.4%. The 1,000 surname sample showed a growth rate of 28.5%. [That's] statistically insignificant. So I'm not sure whether to keep running 1,000 surname queries per day or just stick with 100. Yesterday, the number of users with the 1,000 surnames jumped from 23,922 (all counted by hand) to 24,990, for an increase of 4.47%. I tried to get the count a full day after the original count, but there is no way to make sure that my data entry team can time it exactly right. The counts could be off by several hours, cutting into the accuracy."

• Meanwhile, Google is killing off Google Labs, its experimental area where it released potential products to see how users liked them.

The move is part of a refocus on tighter product releases, and away from the sometimes haphazard approach to releasing its software.

In a blogpost, the company says that "we're prioritizing our product efforts" and that "we believe that greater focus is crucial if we're to make the most of the extraordinary opportunities ahead."

Google Labs contains a huge range of products and ideas, some in nascent form. Among the engineers working on it are Andy Hertzfeld, a former Apple staffer who worked on some of the first Macintosh designs and was closely involved in the design of Google+ .