I've just been introduced to a rather extra-ordinary number: 142857.

Now as it stands, it doesn't look particularly fascinating or special but it does when you start to play with it. So lets get playing.

Lets start with some multiplication...

          142857 x 1 = 142857
          142857 x 2 = 285714
          142857 x 3 = 428571
          142857 x 4 = 571428
          142857 x 5 = 714285
          142857 x 6 = 857142

Oooooooo, well look at that. Do you see it?

Notice how each answer contains exactly the same individual numbers, just shifted slightly. It's easier to see if I list the lines as follows:

          142857 x 1 = 142857
          142857 x 3 = 428571
          142857 x 2 = 285714
          142857 x 6 = 857142
          142857 x 4 = 571428
          142857 x 5 = 714285

Coool.

Now what about multiplying it by 7?

          142857 X 7 = 999999

Whoops!! Don't worry, it's not over. That's actually quite significant. Look what happens when you split the digits into pairs or triplets and add them up:

          142 + 857 = 999
          14 + 28 + 57 = 99

Hmmmm. Interesting. 9s. But what about multiples greater than 7? Well, there's a pattern there too...

          142857 × 8 = 1142856
          142857 × 9 = 1285713
          142857 x 26 = 3714282
          142857 x 142857 = 20408122449
          142857 × 133 = 18999981

See it? Probably not, but you will when I tell you the secret: add the last six digits to the remaining digits and repeating this process until you have only six digits left...

          1 + 142856 = 142857
          1 + 285713 = 285714
          3 + 714282 = 714285
          20408 + 122449 = 142857
          18 + 999981 = 999999

Whoops, that last one didn't work. Or did it? What's significant about 133? It's a multiple of 7. Hmmmm, that number 7 seems to be quite significant, and indeed it is... look what 1 ÷ 7 gives you...

          1 ÷ 7 = 0 . 142857 142857 142857 142857 142857 142857 14...

Well look at that, a never ending list of our magic number.

So what's so special about 142857? Well, according to Wikipedia it's the best-known cyclic number in base 10 (the number system we use). If you multiply the number by 2, 3, 4, 5, or 6, the answer will be a cyclic permutation of itself.

Now wasn't that interesting? Now I've finished amazing you with my random findings, back to work.