Game publishing company Electronic Arts‘ newest social game, The Sims Social, has passed social gaming supergiant Zynga’s Farmville and now has 36 million monthly active users just under a month after its launch, according to AppData.

The Sims Social has held the top spot as the fastest growing application on Facebook for more than a week. The game picked up more than 1.7 million new users on Sunday, and picked up a total of about 8.3 million new users last week. It’s seen enough growth to knock off FarmVille and become the fourth most popular social game on Facebook, behind Zynga’s own Empires & Allies, Cityville and Texas HoldEm Poker. Zynga’s Farmville now has 35.7 million monthly active users.

Electronic Arts is now the second top Facebook app developer with 77.8 million monthly active users. Its well behind Zynga’s 273 million monthly active users, but it’s much further than the next closest social game maker Wooga, which has nearly 40 million monthly active users across all its games.  Before The Sims Social launched, Electronic Arts had around 29 million monthly active users, according to AppData.

Electronic Arts’ newest social game looks like it will give Zynga — which hasn’t really faced any stiff competition in Facebook games — a run for its money. That’s because the game has a massive franchise and name behind it, along with a development team that has a pretty stellar track record. EA has sold more than 140 million copies of the The Sims and its sequels and expansion packs and has generated around $3 billion in revenue from it.

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The Sims Social is basically a lightweight version of The Sims built into a browser on Facebook. The team behind The Sims and casual games maker Playfish both worked on the game. Electronic Arts bought Playfish in 2009 when it was vying with social games maker Zynga for the top social gaming spot. Zynga has since lurched ahead and claimed the top spot.

The Sims was a smash hit with casual gamers because it was a very light game that was easy to get into and offered a lot of depth. You basically control a “sim” as it lives its life and try to achieve lifetime goals — which lets gamers accomplish whatever they want to do in the game.  The games are known for having tongue-in-cheek humor and sharp writing.

Electronic Arts has not-so-quietly established a fierce casual and social gaming team. The company bought Playfish back in 2009 and also bought casual games maker PopCap for $750 million. Both teams have made successful games, and once the PopCap deal closes, there’s a good chance Playfish will be working with casual games maker PopCap.

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