[QUOTE=fetofs]As you proposed many properties on 57, I'll post more numbers:
293
295
297

Note:The site Flatlander posted says that 57=111 in base 9.[/QUOTE]


oops sorry missed this one. Or rather three.

[QUOTE=mfgoode]
So here is the official name of Libya.

"Al Jumahiriyah al Arabiyah al Libiyah ash Shabiyah al Ishtirakiyah".

Try not to be petty and attempt to count the letters. The chances are that on the first trial you will get either 56 or 57 or even 58. Is it worth waisting time and proving and saying that 'U have typed it wrong?'
[/QUOTE]

I didn't mind to read the first part, but a computer can surely count the letters (57).

Special whole numbers
 

[QUOTE=fetofs]As you proposed many properties on 57, I'll post more numbers:
293
295
297

Note:The site Flatlander posted says that 57=111 in base 9.[/QUOTE]
:surprised ;
Allow me to correct you fetofs. Its 57 =111 base 7 as one look at it can tell you so.
Richard (cameron) I dont use the word pedantic as its too often used by our mentors of this forum. I dont think it applies to you as you are more helpful than displaying your book knowledge. Of the situation we were in, the word 'petty' describes it better. However if you dont like its use may I suggest 'pettyfog' (v) or 'pettifogger' (n) ?
Im glad that my mother tongue (English) is so rich that one can always get the correct word for any situation
As you are fed up with the number 57 we should move on I agree.
Heres another difficult number 226
226
P.S. I have to crack it out myself.
There are about 339 numbers below 1000 that need Iinteresting combinations/ relationships which are not known in its entirety or too 'elementary'. Any odd number can be described as the difference of two squares and all the above can be reduced that way. Whether this form can be accepted I leave it up to number theorists to either accept or reject as ' too elementary'.
Mally :coffee:

[QUOTE=Flatlander]Here's a nice link:

[url="http://www.stetson.edu/~efriedma/numbers.html"]http://www.stetson.edu/~efriedma/numbers.html[/url][/QUOTE]

:bow: Thank you once again Flatlander for this excellent site you have given. Its just the sort I was looking for. I tried the other sites but with no luck for getting the meaning and relationship of numbers.
I have already sumitted my entry for 1888 and 1988 and acknowledged your introduction of it to me.
I have asked for an acknowledgement from them but so far no reply
Mally :coffee: .

[QUOTE=fetofs]293
295
297[/QUOTE]

293 = largest possible prime bowling score

So I'll extend the queue:

295
297
16421225

Special whole numbers
 

Cheesehead:

:surprised 295 = 5*(30^2 -29^2)

297 is a Kaprekar number

So Ill extend the queue

226

234

16,421,225 :question:

mally :coffee:

[QUOTE=cheesehead]293 = largest possible prime bowling score

So I'll extend the queue:

295
297
16421225[/QUOTE]

This was one of the properties I was thinking of.
There are also 293 ways to give change for a dollar bill (allowing an 1-dollar coin)

Oh, and 2*295+9*295+5*295+1 is prime...

Special whole numbers
 

[QUOTE=fetofs]This was one of the properties I was thinking of.
There are also 293 ways to give change for a dollar bill (allowing an 1-dollar coin)

Oh, and 2*295+9*295+5*295+1 is prime...[/QUOTE]
:surprised : so whats so great about that?
So is 2*295 + 3*295 +17*295 +1 is a prime and a whole host of others.
Mally :coffee:

[QUOTE=mfgoode]:surprised : so whats so great about that?
So is 2*295 + 3*295 +17*295 +1 is a prime and a whole host of others.
Mally :coffee:[/QUOTE]

And what is so great about 5*(30^2-29^2)... It should be some number after all! :grin:

Special whole numbers
 

[QUOTE=fetofs]And what is so great about 5*(30^2-29^2)... It should be some number after all! :grin:[/QUOTE]
:sad: Yeah I suppose so fetofs. But keep it going and Faith will come to us.
Now For Cheesehead's number 16,421,225. Thanks for a thought provoking one.
I do not know how you arrived at it but here is my interpretation of it.

16,421.225 =5^2 * 19 * 181 *191.
These are all primes and each has interesting properties/qualities
We have dealt with 25 in a previous post but I will give it more detail.

25. All,powers of 25 end up with the same digits 25 (not necessarily vice versa )

25 = 4! + 1 ,the only solution of (n - 1) + 1 = n^2. (Liouville).

Fermat's correct assertion 25 = 2^3 -2 as the only square in which 2 is less than a cube

19 : its the 3rd number whose decimal reciprocal is of max length in this case 18 ; 1/19 = 052631 578947 368421 -- 052631- --

19! - 18! +17! -16! --- +1 is a prime.
The only other numbers with this property are 3 ,4,5, 6 ,7 , 8 , 10 , 15 (Guy)
All integers are the sum of at most 19 4th powers

181 a palindromic prime which is strobogrammatic :grin: (big word- look it up !)

191: palindromic prime but not an invertive one. as 161 =7*23.

To carry on the queue
226
234
104729

mally :coffee:





.

But, Mally, I wrote 16421225 without commas. You might check earlier in this thread for somewhat similar numbers. Not all of them were proposed for purely arithmetic reasons. :-)