Number 59649589127497217 is a factor of Fermat number F7

literka · 2013-11-14, 03:24

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.

CRGreathouse · 2013-11-15, 01:37

Code:

Mod(2,59649589127497217)^2^7+1

literka · 2013-11-15, 08:42

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.

c10ck3r · 2013-11-15, 14:16

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?

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

literka · 2013-11-15, 15:10

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.

retina · 2013-11-15, 15:22

Quote:

Originally Posted by literka

In mathematics something computed by a computer is not regarded as a proof.

Oh?

literka · 2013-11-15, 15:27

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.

R.D. Silverman · 2013-11-15, 15:44

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.

literka · 2013-11-15, 16:09

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.

Mini-Geek · 2013-11-15, 16:11

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.

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

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