User blog comment:Swooped me in one hit/slackitack number/@comment-30754445-20170214123647

Your definition of 3↑↑↑↑3 is wrong.

3↑↑↑↑3 is not a power tower of 3↑↑↑3 threes. It is much much much larger than that. The actual number you called "3↑↑↑↑3" is merely 3↑↑↑4.

To get the real 3↑↑↑↑3, you need to take that power-tower and create a new power tower with that many 3's... and then take that power-tower to create another new power tower with that many 3's... and then take that power-tower to create another new power tower with that many 3's... and repeat the entire process 3↑↑↑3 times!

BTW if we use your version of up-arrows all the way down, your final number would actually be far smaller than Graham's number.

I strongly recommend that you take a look at the videos Chronolegend gave you. Up-arrows are covered in the first two.