When Google+ entered open beta Tuesday, meaning anyone can now join the social network, it seemed pretty clear that the move would lead to a rapid increase in user numbers. It wasn’t quite clear how much of an impact the shift to open beta would generate, but Paul Allen thinks he has the answer.

Ancestry.com founder Allen has been publishing his estimates on the number of users Google+ has pretty much since the service launched. He uses a complex methodology of demographics analysis to arrive at his estimates. He suggested that Google+ hit 10 million users 2 weeks after launching (a fact later confirmed by Google CEO Larry Page) before providing other estimates on the growth of the service.

Around 2 weeks ago, Allen estimated that Google+ had around 28.7 million users. However, after Google opened up access to the service, the number of users on Google+ apparently grew by 30 percent in 2 days. On Thursday morning, Allen’s model of analysis showed that Google+ had 37.8 million users — a figure that had increased to 43.4 million by early Thursday evening.

The timing of Google+’s move into open beta has been most interesting, as it has coincided with a wealth of new features being launched by Facebook. One such feature, the new-look News Feed, was met with fury by many Facebook users, some of whom may have switched to Google+ due to their dismay. Timing is everything, as they say in comedy, but it’s too early to tell whether Google+ has delivered a big blow to Facebook with its open beta move through users switching allegiances due to unhappiness over Facebook’s new features.