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On Wednesday 04 June 2003 05:09, Jon Perry wrote:

> From;

>

> http://vedmaths.tripod.com/frame.htm

>

> click Lessons on the left, then Multiplication in the main page, and then

> Nikhilam.

>

> As RSA numbers fall into this scheme of things, does this algorithm have

> any practical use?

>

Of course not, as is the default answer to most of the things you either come

up with, reinvent and claim to be your own, or find out about in the darkest

corners of the web and give pointers to.

The fact that two numbers were randomly chosen in the same range doesn't mean

that they're close to each other. Take two 5 digit numbers x,y chosen at

random, for instance. That means 10000 <= x,y < 100000. The likelihood that

the most significant digits of x,y differ by at most 1 is small -- just use a

counting argument, there are 81 possibilities in total and the pairs that

work out are {1,2}, {2,3}, {3,4}, {4,5}, {5,6}, {6,7}, {7,8}, {8,9}, {2,1},

{3,2}, {4,3}, {5,4}, {6,5}, {7,6}, {8,7}, {9,8} or 16 possibilities. That

means less than 20% of all 5-digit numbers match this constraint. Those that

don't match are guaranteed to have x-y > 10000, which you'll agree to me is

not close to one another at all. If you apply this argument recursively,

you'll realize all but a vanishingly small set of random numbers in

sufficiently large ranges are close together.

Décio

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