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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. |
[code]Mod(2,59649589127497217)^2^7+1[/code]
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[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. |
[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? |
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=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. |
[QUOTE=literka;359375]In mathematics something computed by a computer is not regarded as a proof.[/QUOTE]Oh?
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[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. |
[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. |
[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. |
[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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