Determine sample size to get a statistically significant result

Hello, this question concerns the topic of A/B split-testing. More about it on wiki here.

I need to determine what is sample size would I require to get a statistically significant result for my experiment. I can see how an economist at Google is doing it. However, our don't understand the steps he takes in order to determine this.

Here is the quote from Google Analytics Help:
"Suppose you’ve got a conversion rate of 4% on your site. You experiment with a new version of the site that actually generates conversions 5% of the time. You don’t know the true conversion rates of course, which is why you’re experimenting, but let’s suppose you’d like your experiment to be able to detect a 5% conversion rate as statistically significant with 95% probability. A standard power calculation(1) tells you that you need 22,330 observations (11,165 in each arm) to have a 95% chance of detecting a .04 to .05 shift in conversion rates. Suppose you get 100 sessions per day to the experiment, so the experiment will take 223 days to complete. In a standard experiment you wait 223 days, run the hypothesis test, and get your answer."

Could someone, please, guide me through how he got to the number of 22,300 observations?

Thank you in advance!