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-   -   Number 59649589127497217 is a factor of Fermat number F7 (https://www.mersenneforum.org/showthread.php?t=18877)

 literka 2013-11-14 03:24

Number 59649589127497217 is a factor of Fermat number F7

Recently I have written a page [URL="http://www.literka.addr.com/mathcountry/numth/proof4.htm"]http://www.literka.addr.com/mathcountry/numth/proof4.htm[/URL] 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 [URL="http://www.literka.addr.com/mathcountry"]http://www.literka.addr.com/mathcountry[/URL].
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.

 CRGreathouse 2013-11-15 01:37

[code]Mod(2,59649589127497217)^2^7+1[/code]

 literka 2013-11-15 08:42

[QUOTE=CRGreathouse;359327][code]Mod(2,59649589127497217)^2^7+1[/code][/QUOTE]

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

 c10ck3r 2013-11-15 14:16

[QUOTE=literka;359355]You should write at least few words. I am not going to try to understand your post. Read my previous posts.[/QUOTE]
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?

 retina 2013-11-15 14:47

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[/code]

 literka 2013-11-15 15:10

[QUOTE=c10ck3r;359368]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?[/QUOTE]

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.

 retina 2013-11-15 15:22

[QUOTE=literka;359375]In mathematics something computed by a computer is not regarded as a proof.[/QUOTE]Oh?

 literka 2013-11-15 15:27

[QUOTE=retina;359376]Oh?[/QUOTE]

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.

 R.D. Silverman 2013-11-15 15:44

[QUOTE=literka;359377]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.[/QUOTE]

BZZT. Wrong.

Thank you for playing.

 literka 2013-11-15 16:09

[QUOTE=R.D. Silverman;359378]BZZT. Wrong.

Thank you for playing.[/QUOTE]

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.

 Mini-Geek 2013-11-15 16:11

[QUOTE=retina;359372]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[/code][/QUOTE]

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 [I]did[/I] 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.

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