On Fermat's Last Number
 

[QUOTE=rajula;319249]Batalov: with this speed you will factorize all the Fermat numbers before Christmas! :skiing:[/QUOTE]
Yes, I'm sure Sergei will factorize [B][I]all [/I][/B]Fermat numbers, regardless of how long it takes to prove primality for the infinite number of infinitely large numbers...:rant::bangheadonwall:

[QUOTE=c10ck3r;319260]Yes, I'm sure Sergei will factorize [B][I]all [/I][/B]Fermat numbers, regardless of how long it takes to prove primality for the infinite number of infinitely large numbers...:rant::bangheadonwall:[/QUOTE]

Luckily there are zero [B]infinitely[/B] large numbers. :popcorn:

[QUOTE=rajula;319305]Luckily there are zero [B]infinitely[/B] large numbers. :popcorn:[/QUOTE]
Ah. So, how many base 10 digits in the [U][I][B]last[/B][/I][/U] Fermat number?

[QUOTE=c10ck3r;319327]Ah. So, how many base 10 digits in the [U][I][B]last[/B][/I][/U] Fermat number?[/QUOTE]

[B]Any[/B] last Fermat number has 42 digits in base 10.

[QUOTE=rajula;319328][B]Any[/B] last Fermat number has 42 digits in base 10.[/QUOTE]

Say what now? F24 is a composite of over 5,000,000 digits base 10.
5000000 != 42

Not a counter-example, c10ck3r, as F24 is not the or a [U]last[/U] Fermat number.

Yes, but they continue to grow exponentially, no?

Yes, doubly-exponentially in the index, in fact!

so, 5050446*2^x> 42, when x>1

This is correct for every integer x > 1, but not for the last one.

I think "[B]42[/B]" is the answer to the question of the meaning of life and everything in [I][URL="http://en.wikipedia.org/wiki/The_Hitchhiker%27s_Guide_to_the_Galaxy"]The Hitchhiker's Guide to the Galaxy[/URL],[/I] maybe that's what rajula is referring to? :smile: