World!Of
Numbers

WON plate
180 |

[ November 22, 2011 ]
A distinct palindrome becoming a product of two pandigitals
B.S. Rangaswamy (email)

I was enthralled to glance through 1277 'nineteen_digit' palindromes
as products of two pandigitals. (See WONplate 115)
I highly commend your effort and patience while discovering these
in collaboration with Peter Kogel.

At this instance, I intend to share the following finding with you
When 6 * 1014 + 3 * 108 is added to a distinct
20_digit palindrome, it becomes a product of two pandigitals !

 ``` 12646681200218664621 + 600000300000000 = 12647281200518664621 2961408357 * 4270698153 ```

In my opinion, there can be a thousand or even more of these
20_digit palindromes, resulting as direct products of two pandigitals.
This phenomenon may be explored in the near future,

The nicest ones will be displayed on this wonplate ! (pdg)

An email from B.S. Rangaswamy arrived at [ August 2, 2012 ]

" I got involved in this stupendous venture during the visit to my son
in Phoenix US in May/July 2012 and arrived at a few hints, which may
be of use to you and interested readers.
Since the search is for 20_digit palindromic products which should be
Evenly Divisible By 11, at least one of the pandigital factor is to be
EDB 11. With this I have developed an Excel Anvil to read certain
eligible products. It was possible to arrive at some Eighters not
Tenners so far. Niners do not exist due to least difference being 11.
With Eighter we mean that 8 out of the 10 digits (left vs right part)
are matching. I have dozens of eighters. Closest products found are:

3150487269 * 3406785129 = 1073303317 7133022701
( Dt 24.05.2012 and Deviation = +11000 )

3170426589 * 3428176509 = 1086878195 5918797801
( Dt 05.07.2012 and Deviation = -11000 )
(3406785129 & 3170426589 are EDB 11)

3472680519 * 3174250869 = 1102315915 5195121011
( Dt 20.09.2012 and Deviation = +11000 )

3621047859 (EDB 11) * 3104865729 = 1124286740 0477924211
( Dt 12.12.2012 (notice its rep_bi_digitality)
and difference of -1100000 )

3571604289 (EDB 11) * 3201586479 = 1143480000 0000808431
( Dt 20.12.2012 (notice the repdigital date)
This Sevenner yields a difference of +34980, a multiple of 11.

3876542109 (EDB 11) * 3247185069 = 1258784965 5694570521
( Dt 07.02.2013)
This Eighter has a difference of +308,000.

With such manual programming, it requires over thousand Full Moon
days to glance through all combinations. Suitably designed Computer
programming is essential to attempt and tackle this uphill task."

A000180 Prime Curios! Prime Puzzle
Wikipedia 180 Le nombre 180
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