Good luck with that, Dan.
In May 2012, Dan will embark on his biggest journey to date, as he attempts a Global Triathlon – swimming, cycling and running around the world. This will include a grueling 5700km swim, as Dan attempts to become the first man in history to swim the Atlantic. …
How do you swim the Atlantic?
One stroke at a time.
Click PLAY or watch it on YouTube.
(via Alister Humphries)
besthike.com 
I always have a problem with things like this when the speed of the person is small when compared to the current they are swimming in. I think someone else claimed to have swam the Atlantic, Benoit Lecomte, but was suspected to have covered more distance while he was sleeping than when swimming.
From wikipedia:
Controversy
Since there is no standard definition of the feat “swimming across the Atlantic”, there is uncertainty about the distance that Lecomte actually covered swimming in the water rather than riding in a boat: according to the Rocky Mountain News, Lecomte would have had to average 8 mph to have swum the entire distance, 3-4 times as fast as other long-distance swimmers.