On Fermat's Last Number

c10ck3r · 2012-11-21, 23:29

Quote:

Originally Posted by rajula

Batalov: with this speed you will factorize all the Fermat numbers before Christmas!

Yes, I'm sure Sergei will factorize all Fermat numbers, regardless of how long it takes to prove primality for the infinite number of infinitely large numbers...

rajula · 2012-11-22, 08:12

Quote:

Originally Posted by c10ck3r

Yes, I'm sure Sergei will factorize all Fermat numbers, regardless of how long it takes to prove primality for the infinite number of infinitely large numbers...

Luckily there are zero infinitely large numbers.

c10ck3r · 2012-11-22, 14:45

Quote:

Originally Posted by rajula

Luckily there are zero infinitely large numbers.

Ah. So, how many base 10 digits in the last Fermat number?

rajula · 2012-11-22, 15:01

Quote:

Originally Posted by c10ck3r

Ah. So, how many base 10 digits in the last Fermat number?

Any last Fermat number has 42 digits in base 10.

c10ck3r · 2012-11-22, 15:26

Quote:

Originally Posted by rajula

Any last Fermat number has 42 digits in base 10.

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

akruppa · 2012-11-22, 15:47

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

c10ck3r · 2012-11-23, 22:56

Yes, but they continue to grow exponentially, no?

akruppa · 2012-11-23, 23:22

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

c10ck3r · 2012-11-23, 23:44

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

akruppa · 2012-11-26, 12:07

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

aketilander · 2012-11-28, 21:53

I think "42" is the answer to the question of the meaning of life and everything in The Hitchhiker's Guide to the Galaxy, maybe that's what rajula is referring to?

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2012-11-22, 15:47	#6
akruppa "Nancy" Aug 2002 Alexandria 2,467 Posts	Not a counter-example, c10ck3r, as F24 is not the or a last Fermat number.

2012-11-23, 22:56	#7
c10ck3r Aug 2010 Kansas 547 Posts	Yes, but they continue to grow exponentially, no?

2012-11-23, 23:22	#8
akruppa "Nancy" Aug 2002 Alexandria 4643₈ Posts	Yes, doubly-exponentially in the index, in fact!

2012-11-23, 23:44	#9
c10ck3r Aug 2010 Kansas 547 Posts	so, 5050446*2^x> 42, when x>1

2012-11-26, 12:07	#10
akruppa "Nancy" Aug 2002 Alexandria 2,467 Posts	This is correct for every integer x > 1, but not for the last one.

2012-11-28, 21:53	#11
aketilander "Åke Tilander" Apr 2011 Sandviken, Sweden 2·283 Posts	I think "42" is the answer to the question of the meaning of life and everything in The Hitchhiker's Guide to the Galaxy, maybe that's what rajula is referring to?