I give you the number: 3

Can you remember it? Of course, what a stupid question.

And 31?
What about 314?
Still easy? Yes?
And 31490?
Should be able to do it.
And 314903204958430039452214545?
Now it is getting a bit more challenging, is it not?
What about a list of numbers with 1500 digits in it? Think it is possible? Well, yes, it is!
What if I give you?:
Would you be able to memorise this table with a set of red numbers within three minutes so that you can recall it by giving the number in any block, say 1E, or row 1 backwards or column B from the bottom! Think it can be done? I bet you it can.

The proof I have that this memory technique works is from my own experience with presenting study courses. I once had a one-on-one course with a junior school student. We started on a Wednesday. The first thing I did was to show her how to memorise a table like this. I then asked her to fill the numbers in and I memorised the set of numbers. I then gave her the piece of paper and told her I would not think of it again and I did cut it out of my brain, never thought of it again. The Monday afternoon I asked her to get the piece of paper and test me without me revising it at all. I could recall the table perfectly, and in any sort of order she wanted to ask me. Good, I've won my bet!
To memorise long numbers we again need to have some sort of system. This we find in what is known as Pegging. This is a very old system already used by the Greeks, but in modern times used and adapted by people such as Tony Buzan with his Mind Maps.

You are already familiar with Visualisation and the Link System, and we use the same idea to remember numbers, namely to create pictures or images and link them to the numbers.

The idea of this system is to give a number a phonetic sound value of the consonants and these sounds are then joined to form words, and these words are then linked to form images.

I can hear you say that this sounds very confusing, so, let me show you how this works.
I am a brain, Watson. The rest of me is a mere appendix.
Arthur Conan Doyle
The Number Phonetic System