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.

```          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.