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 2013-11-14, 03:24 #1 literka     Mar 2010 26·3 Posts Number 59649589127497217 is a factor of Fermat number F7 Recently I have written a page http://www.literka.addr.com/mathcoun...mth/proof4.htm with a proof that59649589127497217 is a factor of Fermat number F7. It is something similar to my previous work about F5 and F6 (see my posts in this section "Factoring" or visit my description page http://www.literka.addr.com/mathcountry. Unfortunately factors of F7 are large numbers, hence some computation had to be with numbers of same size. Still these numbers are incomparably smaller than F7. Last fiddled with by literka on 2013-11-14 at 03:26
 2013-11-15, 01:37 #2 CRGreathouse     Aug 2006 3·1,993 Posts Code: Mod(2,59649589127497217)^2^7+1
2013-11-15, 08:42   #3
literka

Mar 2010

C016 Posts

Quote:
 Originally Posted by CRGreathouse Code: Mod(2,59649589127497217)^2^7+1

You should write at least few words. I am not going to try to understand your post. Read my previous posts.

2013-11-15, 14:16   #4
c10ck3r

Aug 2010
Kansas

547 Posts

Quote:
 Originally Posted by literka You should write at least few words. I am not going to try to understand your post. Read my previous posts.
He was giving a simple code to accomplish the same thing as your proof. Except his version goes straight to (11) in yours, negating the need for, well, your entire "proof". Might I ask why you are "proving" known Fermat divisors? Do you think this will give some unknown insight into Fermat divisors to allow one to predict what unknown divisors are?

 2013-11-15, 14:47 #5 retina Undefined     "The unspeakable one" Jun 2006 My evil lair 22×1,553 Posts Even one my my lessor minions can do this longhand Code:  5704689200685129054721 ---------------------------------------- 59649589127497217)340282366920938463463374607431768211457 298247945637486085||||||||||||||||||||| ------------------||||||||||||||||||||| 420344212834523784|||||||||||||||||||| 417547123892480519|||||||||||||||||||| ------------------|||||||||||||||||||| 279708894204326563|||||||||||||||||| 238598356509988868|||||||||||||||||| ------------------|||||||||||||||||| 411105376943376953||||||||||||||||| 357897534764983302||||||||||||||||| ------------------||||||||||||||||| 532078421783936517|||||||||||||||| 477196713019977736|||||||||||||||| ------------------||||||||||||||| 548817087639587814||||||||||||||| 536846302147474953||||||||||||||| ------------------||||||||||||||| 119707854921128616|||||||||||||| 119299178254994434|||||||||||||| ------------------|||||||||||||| 408676666134182074||||||||||| 357897534764983302||||||||||| ------------------||||||||||| 507791313691987723|||||||||| 477196713019977736|||||||||| ------------------|||||||||| 305946006720099871||||||||| 298247945637486085||||||||| ------------------||||||||| 76980610826137867|||||||| 59649589127497217|||||||| -----------------|||||||| 173310216986406506||||||| 119299178254994434||||||| ------------------||||||| 540110387314120728|||||| 536846302147474953|||||| ------------------|||||| 326408516664577521|||| 298247945637486085|||| ------------------|||| 281605710270914361||| 238598356509988868||| ------------------||| 430073537609254934|| 417547123892480519|| ------------------|| 125264137167744155| 119299178254994434| ------------------| 59649589127497217 59649589127497217 ----------------- 0
2013-11-15, 15:10   #6
literka

Mar 2010

26·3 Posts

Quote:
 Originally Posted by c10ck3r He was giving a simple code to accomplish the same thing as your proof. Except his version goes straight to (11) in yours, negating the need for, well, your entire "proof". Might I ask why you are "proving" known Fermat divisors? Do you think this will give some unknown insight into Fermat divisors to allow one to predict what unknown divisors are?

It is proof not a "proof". The purpose is obvious, so obvious that I did not mention if: to find a proof that something is a factor with no help of a computer and avoid time-consuming computations as presented by Retina.
In mathematics something computed by a computer is not regarded as a proof. This problem arose with a "proof" of Four Colors Theorem. Many mathematicians regarded this as not a proof because of intense using of computers.
I suspect that my proof of F7 is not best possible i.e. there must be a proof more straightforward, using less computations.

Last fiddled with by literka on 2013-11-15 at 15:12

2013-11-15, 15:22   #7
retina
Undefined

"The unspeakable one"
Jun 2006
My evil lair

22×1,553 Posts

Quote:
 Originally Posted by literka In mathematics something computed by a computer is not regarded as a proof.
Oh?

2013-11-15, 15:27   #8
literka

Mar 2010

26·3 Posts

Quote:
 Originally Posted by retina Oh?

Maybe I exaggerated a little bit. It should be:
In mathematics something computed by a computer is not regarded as a proof by most of mathematicians.

2013-11-15, 15:44   #9
R.D. Silverman

Nov 2003

22×5×373 Posts

Quote:
 Originally Posted by literka Maybe I exaggerated a little bit. It should be: In mathematics something computed by a computer is not regarded as a proof by most of mathematicians.
BZZT. Wrong.

Thank you for playing.

2013-11-15, 16:09   #10
literka

Mar 2010

26·3 Posts

Quote:
 Originally Posted by R.D. Silverman BZZT. Wrong. Thank you for playing.

I don't want to ague with you about it, it is not a subject of this post. No statistics is made. I heard the story, but it is only a story, I am not sure that it is a true story. And the story is this:
Long time ago it was announced that a proof of Four Colors Theorem was found. It was presented in Finland and I talked to mathematicians, who were there. They did not accept this proof because of use of computers. They even told that the method was known long before. Presenters just wrote a program to verify what was known before.
This is everything I know about it. I heard this from a second hand so I cannot be sure that it is true.

2013-11-15, 16:11   #11
Mini-Geek
Account Deleted

"Tim Sorbera"
Aug 2006
San Antonio, TX USA

17×251 Posts

Quote:
 Originally Posted by retina Even one my my lessor minions can do this longhand Code:  5704689200685129054721 ---------------------------------------- 59649589127497217)340282366920938463463374607431768211457 298247945637486085||||||||||||||||||||| ------------------||||||||||||||||||||| 420344212834523784|||||||||||||||||||| 417547123892480519|||||||||||||||||||| ------------------|||||||||||||||||||| 279708894204326563|||||||||||||||||| 238598356509988868|||||||||||||||||| ------------------|||||||||||||||||| 411105376943376953||||||||||||||||| 357897534764983302||||||||||||||||| ------------------||||||||||||||||| 532078421783936517|||||||||||||||| 477196713019977736|||||||||||||||| ------------------||||||||||||||| 548817087639587814||||||||||||||| 536846302147474953||||||||||||||| ------------------||||||||||||||| 119707854921128616|||||||||||||| 119299178254994434|||||||||||||| ------------------|||||||||||||| 408676666134182074||||||||||| 357897534764983302||||||||||| ------------------||||||||||| 507791313691987723|||||||||| 477196713019977736|||||||||| ------------------|||||||||| 305946006720099871||||||||| 298247945637486085||||||||| ------------------||||||||| 76980610826137867|||||||| 59649589127497217|||||||| -----------------|||||||| 173310216986406506||||||| 119299178254994434||||||| ------------------||||||| 540110387314120728|||||| 536846302147474953|||||| ------------------|||||| 326408516664577521|||| 298247945637486085|||| ------------------|||| 281605710270914361||| 238598356509988868||| ------------------||| 430073537609254934|| 417547123892480519|| ------------------|| 125264137167744155| 119299178254994434| ------------------| 59649589127497217 59649589127497217 ----------------- 0
I'd be impressed if a "lesser minion" could do that longhand without making a mistake. Shoot, I'd be impressed if a mathematician could do that longhand without making a mistake (for that matter, just how did mathematicians, like Lucas with M127, do enormous calculations way-back-when?). It's far easier to trust a computer.
Since you're already working from the prior knowledge that the factor exists, why not take both factors and multiply them together? That'd be a much less difficult feat.

Last fiddled with by Mini-Geek on 2013-11-15 at 16:16

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