Integer 6643 joins the World!Of Palindromes !

but not through our trustworthy base 10 numbersystem since ...
we first have to convert the number into base 9
before we can reveal the hidden beauty !

6643¹ = 10101_{9}
6643² = 102030201_{9}
6643³ = 1030607060301_{9}

and that  10101³ = 102030201^3/2 = 1030607060301¹ in base 10 !

Moreover 6643 is also palindromic in the following bases

6643 = 10101_{9}
6643 = 100010001_{3}
6643 = 1100111110011_{2}

The digits of 6643 are in descending order.
If we do the same with its prime factors 7, 13 and 73 we get

6643 = 73 x 13 x 7

or when concatenated we get the palindrome 73137

Multiplicand 6643 smallest multiplier to arrive at
a palindromic product is... another palindrome

6643 x 44 = 292292

A connection with palindrome 3773
The smallest probable prime (prp) larger than 10³⁷⁷³ is

10³⁷⁷³ + 6643

Here follows a list of borderprp's with nonpalindromic exponents included :

Can you help extend the list of 6643 written out in various languages ?

[ August 22, 2001 ]
Terry Trotter, speaking as a school teacher of math, always asked the students
not to use 'and' except when stating things like '3.14' [three and fourteen hundredths].
That is, to indicate the decimal point.
Also for numbers between 20 and 100, like 43, 78, 55, etc. a hyphen [-] is required.
forty-three, seventy-eight, etc. Realizing manners are different in different
countries, for Terry, 6643 should be written as follows