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The most mysterious numbers

The most mysterious numbers are 6174,  142857 and 19790509. Do you know why?

6174

The number 6174 is a really mysterious number. At first glance, it might not seem so obvious. But as we are about to see, anyone who can subtract can uncover the mystery that makes 6174 so special.

Kaprekar’s operation

In 1949 the mathematician D. R. Kaprekar from Devlali, India, devised a process now known as Kaprekar’s operation. First choose a four digit number where the digits are not all the same (that is not 1111, 2222,…). Then rearrange the digits to get the largest and smallest numbers these digits can make. Finally, subtract the smallest number from the largest to get a new number, and carry on repeating the operation for each new number.

It is a simple operation, but Kaprekar discovered it led to a surprising result. Let’s try it out, starting with the number 2005, the digits of last year. The maximum number we can make with these digits is 5200, and the minimum is 0025 or 25 (if one or more of the digits is zero, embed these in the left hand side of the minimum number). The subtractions are:

5200 – 0025 = 5175
7551 – 1557 = 5994
9954 – 4599 = 5355
5553 – 3555 = 1998
9981 – 1899 = 8082
8820 – 0288 = 8532
8532 – 2358 = 6174
7641 – 1467 = 6174

When we reach 6174 the operation repeats itself, returning 6174 every time. We call the number 6174 a kernel of this operation. So 6174 is a kernel for Kaprekar’s operation, but is this as special as 6174 gets? Well not only is 6174 the only kernel for the operation, it also has one more surprise up its sleeve. Let’s try again starting with a different number, say 1789.

9871 – 1789 = 8082
8820 – 0288 = 8532
8532 – 2358 = 6174

We reached 6174 again!
6174: a very mysterious number…

A very mysterious number…

When we started with 2005 the process reached 6174 in seven steps, and for 1789 in three steps. In fact, you reach 6174 for all four digit numbers that don’t have all the digits the same. It’s marvellous, isn’t it? Kaprekar’s operation is so simple but uncovers such an interesting result. And this will become even more intriguing when we think about the reason why all four digit numbers reach this mysterious number 6174.

142857

Okay, it’s just a number, right? But did you know that when it is multiplied and manipulated, it displays some really amazing properties? For example:
142,857 x 1 = 142,857
142,857 x 2 = 285,714
142,857 x 3 = 428,571
142,857 x 4 = 571,428
142,857 x 5 = 714,285
142,857 x 6 = 857,142

Did you notice anything?
It’s always the same numbers moving along as if on a ribbon… simply amazing, huh?

And how about
142,857 x 7 = 999,999
And if we add 142 + 857= 999
And if we add 14 + 28 + 57= 99

Or
142,857 x 142,857 = 20,408,122,449
Then
20,408 + 122,449 = 142,857

And how about
142,857 x 8 = 1,142,856
Remove the first digit (1) and add it to the last digit (6) and we get 142,857

And how about
142,857 x 9 = 1,285,713
Remove the last digit (3) and add it to the first digit (1) and then move the second to last digit (1) to the front and we get 142,857

And how about
142,857 x 11 = 1,571,427
Remove the first digit (1) and add it to the last digit (7) and then move the second and third digit (5,7) to the end and we get 142,857

And how about
142,857 x 12 = 1,714,284
Take the first digit (1) and add it to the last digit (4) and then move the second digit (7) to the end and we get 142,857

And how about
142,857 x 15 = 2,142,855
Remove the first digit (2) and add it to the last digit (5) and we get 142,857

Can you discover some more interesting mathematical manipulations involving 142,857?

19790509

The infamous Stuxnet worm continues to capture the imagination of the general public, with theories that it was written to target nuclear plants inside Iran.

One of the so-called clues that is frequently rolled out in articles about Stuxnet is the mysterious string of characters that the worm leaves inside the Registry on infected Windows computers:

19790509

Most commentators have decided to read this as a date – namely, 9th of May, 1979.

Clearly the date isn’t being used by the worm as a trigger for a payload, as it’s over thirty years ago in the past. Instead, it’s used by the Stuxnet malware to tell whether it has already infected a computer.

It feels like everyone is focusing on the fact that a Jewish Iranian businessman, Habib Elghanian, was executed by a firing squad in Tehran on May 9 1979, and like to link it with the marker inside the Stuxnet worm.

But should we be a little more cautious and look for something more than circumstantial evidence before treating the characters 19790509 like that?

Rosario Dawson

After all, 9th May 1979 is also the birthday of actress Rosario Dawson.

Come on, you must know her – she was in Kids, Men in Black II and the recent Percy Jackson & The Lightning Thief movie.

She even speaks a little Klingon.

With a pedigree like that surely she’s a prime candidate for some geek lust, and an obsessed fan might be tempted to embed her date of birth into a piece of malware?

Or maybe Stuxnet’s author is a huge fan of “The Grateful Dead”? Perhaps his favourite record is a bootleg of their 9th May 1979 concert at Broome County Arena, Binghamton, NY, where they sang “China Cat Sunflower”, “Friend of the Devil” and “Wharf Rat” amongst others?

Or could it be that the mysterious creator of Stuxnet is not commemorating the death of Habib Elghanian, but instead the passing of multi-millionaire Cyrus S Eaton, composer Lan Adomian, jazz vocalist Eddie Jefferson, and Australian politician Sir Charles Adermann? All of whom also died on 9th May 1979.

All this is assuming, of course, that 19790509 is a date in the form “yyyymmdd”.

It could equally have been the coder’s preferred Bingo numbers (19, 79, 05, 09).

Or, it could be that whoever wrote Stuxnet liked to use the date format “yyyyddmm” which would mean that we’re all focusing on the wrong date entirely.

(By the way, although rare, there are programs which appear to use the ‘yyyyddmm’ date format – just Google it)

If the coder had adopted the ‘yyyyddmm’ date format then that would mean we should be considering 5th September 1979 instead.

Scrabble keyboard
Which just happens to be the birthday of footballers John Carew (Norwegian), George O’Callaghan (Irish) and Salvatore Mastronunzio (Italian). Additionally, according to Wikipedia, it’s the date of birth of Stacey Dales (a Canadian basketball player and sportscaster) and English scrabble player Stewart Holden.

Hmm..

I imagine there are thousands of different interpretations we could give to the number 19790509, and maybe we should be a little more cautious of jumping to conclusions. After all, it could just as easily be the creator’s own date of birth, or his parent’s wedding day, or an entirely randomly chosen number.

Unless we find whoever is responsible for Stuxnet, my guess is that no-one will ever know for sure.


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