Back in April, Twitter’s Jack Dorsey announced that his newest venture, Square Inc was already processing about $5 billion worth of transactions per year, and being used at almost 10,000 stores around the country.

Today, that number has doubled and Square is an accepted form of payment at over 20,000 outlets nationwide.

For about ten bucks you can go to Walmart, Target, or Best Buy and get a Square reader for your iPhone, iPad, or Android device. There’s even an app that will let you pay at some shops just by telling the cashier your name. Pretty impressive! I guess that’s why they have over one million registered customers.

But Square still has some pretty stiff competition to overcome by their biggest rival, PayPal. While payments on Square cost 2.75%, PayPal charges only 2.7% and it doesn’t require merchants to purchase any additional equipment. Payments are processed using either a PayPal card or a phone number and PIN ID.

Also, PayPal’s latest initiative has them partnered with 15 extremely popular retailers including Abercrombie & Fitch, Advance Auto Parts, Aéropostale, American Eagle Outfitters, Barnes & Noble, Foot Locker, Guitar Center, Jamba Juice, JC Penney, Jos. A. Bank Clothiers, Nine West, Office Depot, Rooms To Go, Tiger Direct and Toys “R” Us.

So there’s some fierce competition to overcome before we can really consider Square Inc. to be a leader in the mobile payments arena, but last we heard, Jack Dorsey was out drumming up interest from prominent investors like Legg Mason and Fidelity, so another big breakthrough could be just on the horizon. We’ll keep you posted.