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Calculation Overload?
It would take a human over an hour to perform the above calculations
at a rate of three single digit additions per second, assuming it was done flawlessly.
A program I created
(running on my 200 MHz AMD-K6 desktop PC)
can perform the above calculations in 0.0006 seconds
(0.6 thousandths of a second).
It was programming in assembly language
- hand coded and optimized in pure computer language -
this is almost as fast as it gets without upgrading hardware
(I have untested theories on how to
improve the algorithm, such as look up tables,
multiple digits stored per byte, etc. There's always
a way to make it go faster . . .).
This program has continued the above sequence to
32,000,000 iterations.
This resulted in a number over 13,000,000 digits long,
which has yet to produce a palindrome.
It took just over 283 days of calculations on a 266 MHz and a
400 MHz desktop machine, running at separate times.
The nature of the algorithm eliminates the option of using
multiple machines to improve its calculation speed
as each iteration depends on the full answer of the last iteration.
(To perform the calculations on multiple machines,
you would need a very reliable high speed connection with minimal latency between the machines,
and a completely new algorithm that allows partial processing of the huge number.
I will not get into it here, but I have some very good ideas regarding this.
If anyone is thinking about moving the 196 Palindrome Quest to a parallel network,
please take a look at the
Processing Across a Network thread,
on the 196 Discussion Board.
You can see my thoughts there.
[Note: This message board is offline.
If anyone is willing to host this message board, so it can continue to exist,
please contact me.
Internet Archive of
Processing Across a Network
thread.])
To give an indication
of how many calculations this actually is, it would take
a human being, at the rate of 3 additions per second, 3,300,000
years to accomplish this working 24 hours a day, 7 days a week,
without any breaks, and assuming the calculations are done flawlessly.
The next goal was 40,000,000 iterations, which would have resulted
in a 16,000,000 digit number taking a little over a year.
But, I stopped the quest at this time, since I no longer had access to
a computer to continue the calculations.
I have passed on my work to
Wade VanLandingham.
On his web site, 196 and Other Lychrel Numbers,
he has continued the quest to over 300,000,000 digits
(almost 725,000,000 iterations).
Please take a look at my
World's Record
page for more information on my involvement in this quest, as well as other palindrome records.
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