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 !

6643^{1} = 10101_{{9}}

6643^{2} = 102030201_{{9}}

6643^{3} = 1030607060301_{{9}}

and that 10101^{3} = 102030201^{3/2} = 1030607060301^{1} 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 10^{3773} is

10^{3773} + 6643

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

10^{3159} + 6643

10^{3773} + 6643

10^{7011} + 6643

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

[Dutch] Zesduizendzeshonderddrieënveertig

[English] Six thousand six hundred and forty three

[French] Six mille six cent quarante trois

[German]---

[Italian]---

[Spanish] Seis mil seiscientos cuarenta y tres

[Other]---

[ *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

[English] Six thousand six hundred forty-three