As you can see on the screen, there are three options. Each option describes what you have to do (such as not getting a question wrong, completing as many questions as you can in 5 minutes, ect.) but that has nothing to do with the questions. When you click on one of the three options you see n the screen, you will be shown a number and will see the question, is this number prime or not, pop up. A prime number is a number that cannot be divided by any number but 1 and itself.
For mode 3, you may have to click on the green flag again before clicking on it for there to be no delay. I do not know what causes the delay.
