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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.

 retina 2013-11-15 16:30

[QUOTE=Mini-Geek;359383]It's far easier to trust a computer.[/QUOTE]Sure. If the hackers/NSA/GCHQ haven't gotten their codez into it.[QUOTE=Mini-Geek;359383]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.[/QUOTE]The more difficult the task the better we become at doing the other tasks. Even so, this is more of a tedious task rather than a hard task.

[size=1][color=white]I considered making him do it in hexadecimal just to show that he understood how hex works but somehow that seemed a little bit too cruel even for me.[/color][/size]

 R.D. Silverman 2013-11-15 17:07

[QUOTE=literka;359381]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]

A little knowledge is a dangerous thing. It is especially applicable in your case. You heard a second hand story, yet you presented the
"computer proof is not accepted by mathematicians" assertion as fact.

The story, as you heard is is half true. But you carefully omitted
relevant facts, probably out of ignorance rather than an attempt at
deceit. Despite this, you still made a bold, incorrect assertion.

 R.D. Silverman 2013-11-15 17:11

[QUOTE=Mini-Geek;359383]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?).
[/QUOTE]

Hugh Williams did a thorough research of this very question.
Lucas used some 'templates' (which were basically analog mechanisms
for simulating binary arithmetic) to speed the arithmetic. Lucas did
the whole calculation in binary.

I heard Hugh give a talk on this. I believe he also put it in his book.
I would have to go look; I am in the office and the book is at home.

 literka 2013-11-15 18:14

[QUOTE=R.D. Silverman;359386]A little knowledge is a dangerous thing. It is especially applicable in your case. You heard a second hand story, yet you presented the
"computer proof is not accepted by mathematicians" assertion as fact.

The story, as you heard is is half true. But you carefully omitted
relevant facts, probably out of ignorance rather than an attempt at
deceit. Despite this, you still made a bold, incorrect assertion.[/QUOTE]

At least I supported my statement with some facts. This what you wrote (your way of thinking) can be reversed for your case. You boldly write that my assertion is incorrect and you give no arguments. You presented a naked statement and you assume this as a fact.
Of course I am using a double standard comparing me with you (it is your double standard theory, which you applied before).

 R.D. Silverman 2013-11-15 18:57

[QUOTE=literka;359390]At least I supported my statement with some facts.
[/QUOTE]

False. You presented no facts.
[QUOTE]

This what you wrote (your way of thinking) can be reversed for your case.
[/QUOTE]

This last sentence is gibberish. Your prose is on a level with your mathematics.

[QUOTE]
You boldly write that my assertion is incorrect and you give no arguments.
You presented a naked statement and you assume this as a fact.

[/QUOTE]

What I wrote is supported by an extensive publication history on the part
of the mathematical community in which computer proof systems have been
developed, used, and discussed. It is only YOUR ignorance of the
literature which leads you to erroneously believe that there is no evidence.

I am part of the mathematical community. I talk
with other mathematicians all the time. I attend conferences where
people talk. I am asked to referee papers where people use computers
as part of their work.

I took part in the active discussion regarding Haken & Appel's proof when
it was first presented. Extensive discussion followed in the 80's over the
Internet. There was never a question of the validity of the proof method.
The only question was about the accuracy of the code that was used and
of the reliability of the computation. Doubts were dispelled when others
performed an independent verification using other computers and source
code.

 Batalov 2013-11-15 19:09

literka,

Could you please present the number of operations needed to carry on all your calculation (1) - (5), etc, compared to a simple multiplication of two factors.

It appears that to assert these:
[CODE]Several equalities will be needed:

(1) p=208648999^2+126945596^2 = 512 * q+1

(2) s = 208648999*52542249 + 126945596*31967597

(3) 126945596*52542249 - 208648999*31967597 = 1

(4) 309*q + r = 2^55

(5) r = (s div 512)+1[/CODE]
one will have to do much more than to simply assert
[CODE]59649589127497217 *
5704689200685129054721
= 340282366920938463463374607431768211457
= 2^128+1[/CODE]

And even less work [I]in octal[/I] (with an octal multiplication table at your side)
[CODE]2^128+1 = 4000000000000000000000000000000000000000001
and then

3237257607274243001
*
1152401672664431414535001
=
4000000000000000000000000000000000000000001[/CODE]

 literka 2013-11-15 19:20

[QUOTE=R.D. Silverman;359394]
This last sentence is gibberish. Your prose is on a level with your mathematics.

What I wrote is supported by an extensive publication history on the part
of the mathematical community in which computer proof systems have been
developed, used, and discussed. .[/QUOTE]

I did not see anything you did in mathematics. At least I did not see any announcement of your achievements in this forum, while I presented new results from time to time. I read your book, but only to check the level of your mathematics.
I am not surprised that people of a community, in which computer proof systems have been developed, used, and discussed, think that computer based proofs must be accepted in mathematics.
Frankly saying I have enough to see your insults. Take care of yourself and don't write in my threads.

 wblipp 2013-11-15 19:27

[QUOTE=literka;359396]I did not see anything you did in mathematics[/QUOTE]

Bob has an extensive publication history, much of it relevant to the factoring topics commonly discussed here. Bob is even mentioned in the Cunningham Book.

Moved to Misc Math.

 literka 2013-11-15 19:33

[QUOTE=Batalov;359395]literka,

Could you please present the number of operations needed to carry on all your calculation (1) - (5), etc, compared to a simple multiplication of two factors.

It appears that to assert these:
[CODE]Several equalities will be needed:

(1) p=2086489992+1269455962 = 512 * q+1

(2) s = 208648999*52542249 + 126945596*31967597

(3) 126945596*52542249 - 208648999*31967597 = 1

(4) 309*q + r = 255

(5) r = (s div 512)+1[/CODE]
one will have to do much more than to simply assert
[CODE]59649589127497217 *
5704689200685129054721
= 340282366920938463463374607431768211457
= 2^128+1[/CODE]

And even less work [I]in octal[/I] (with an octal multiplication table at your side)
[CODE]2^128+1 = 4000000000000000000000000000000000000000001
and then

3237257607274243001
*
1152401672664431414535001
=
4000000000000000000000000000000000000000001[/CODE][/QUOTE]

Go to the page of Wikipedia, where the proof that 641 is a factor of F5. Compute the number of operations in this proof and number number of operations to multiply 641 by 6700417. Page of Wikipedia is not about F5 but about all Fermat numbers. Still, they thought that it is worthy to include proof about the number 641. So, if you have complains, write to Wikipedia first.
And yes, I have new ideas to find proofs corresponding to Fermat numbers with larger indexes.

 literka 2013-11-15 19:40

Bob has an extensive publication history, much of it relevant to the factoring topics commonly discussed here. Bob is even mentioned in the Cunningham Book.

Moved to Misc Math.[/QUOTE]

I understand that you care that nobody should write insults. Silverman wrote that I am crank after I wrote my first post here. I never exceed level of insulting Silverman used with respect to me.

 Batalov 2013-11-15 20:07

[QUOTE=literka;359399]Page of Wikipedia is not about F5 but about all Fermat numbers. [/QUOTE]
Exactly.

[QUOTE=literka;359399]Still, they thought that it is worthy to include proof about the number 641.[/QUOTE]
What proof? What are you talking about?

 literka 2013-11-15 20:22

[QUOTE=Batalov;359404]Exactly.

What proof? What are you talking about?[/QUOTE]

Sorry, no more answers. I am insulted all the time and when I defend myself I am moved to Misc. I made last attempt to be here. Batalov, still I wish you good luck. Bye.

 ewmayer 2013-11-15 23:08

An alternative "proof by dilemma"

[QUOTE=Batalov;359404]What proof? What are you talking about?[/QUOTE]

It seems he's talking about Euler's famous - and untrustworthy, because it relied on Herr Euler's "computation" - proof that 641 divides F5, thus (allegedly and untrustworthily) 'disproving' Fermat's conjecture that all Fn are prime.

Allow me to present a simplified version of CRGreathouse's post #2 "untrustworthy alternative computer-aided proof" - this one can more easily be done by hand, as it breaks things down into a "powering via repeated doubling and addition of 1 to result" step (Lemma 1) and a "multiplication of one number by another" step (Lemma 2). The mathematically fancy-pantsy around here may have heard of "proof by contradiction" (as in "you're wrong, thus I'm right.") ... the structure of my proof below is in the form of 2 lemmas - not to be confused with [url=http://en.wikipedia.org/wiki/Lemming]those furry little critters[/url] who famously and counterfactually have a reputation for mass cliff-diving (and which are close relatives of gerbils, as it happens) - thus "proof by dilemma", as it were.

I hope that said decomposition will make it easier for the mathematical community to organize the extensive independent double-checking effort needed to satisfy the OP of the validity of the (allegedly and untrustworthy) alternative proof.

[b]Lemma 1:[/b] Let n = 2^7. Then n = 128, and F7 := 2^n+1 = 340282366920938463463374607431768211457.

[b]Lemma 2:[/b] F7 = 59649589127497217 x 5704689200685129054721 .

QED

Is that at all understandable? Perhaps we should organize a special conference - is it too late to propose this as a last-minute add-on to this year's WCNTC at Asilomar?

 jyb 2013-11-15 23:21

[QUOTE=Batalov;359404]Exactly.

What proof? What are you talking about?[/QUOTE]

[QUOTE]
The fact that 641 is a factor of F5 can be easily deduced from the equalities 641 = 2[sup]7[/sup]×5+1 and 641 = 2[sup]4[/sup] + 5[sup]4[/sup]. It follows from the first equality that 2[sup]7[/sup]×5 ≡ −1 (mod 641) and therefore (raising to the fourth power) that 2[sup]28[/sup]×5[sup]4[/sup] ≡ 1 (mod 641). On the other hand, the second equality implies that 5[sup]4[/sup] ≡ −2[sup]4[/sup] (mod 641). These congruences imply that −2[sup]32[/sup] ≡ 1 (mod 641).
[/QUOTE]

This does show what it's trying to with only arithmetic on numbers no bigger than 641, which is admittedly somewhat clever. However, I don't think this can claim to be any more of a [I]proof[/I] than simply multiplying the two factors.

 Batalov 2013-11-15 23:31

[QUOTE=jyb;359432]However, I don't think this can claim to be any more of a [I]proof[/I] than simply multiplying the two factors.[/QUOTE]
Exactly.

Similarly, here's a "proof", that 9=3*3.
"Proof": 3*3=(1+2)^2=1^2+2*1*2+2^2=9.
Alleged added value of the "proof": it operates only with numbers no more than 2. While direct multiplication deals with larger numbers (i.e. 3).

 ewmayer 2013-11-16 00:49

[QUOTE=ewmayer;359431][b]Lemma 2:[/b] F7 = 59649589127497217 x 5704689200685129054721 .[/QUOTE]

I have through exhaustive labors succeeded in verifying part 2 of my proof by dilemma. We first tabulate multiples of the larger (purported) multiplicand by 0-9: 5704689200685129054721 x ____ =
[code]
0 0
1 5704689200685129054721
2 11409378401370258109442
3 17114067602055387164163
4 22818756802740516218884
5 28523446003425645273605
6 34228135204110774328326
7 39932824404795903383047
8 45637513605481032437768
9 51342202806166161492489[/code]

And here is the resulting (no FFTs, DWTs or other suspicious 3-letter-initialism-denoted computer flummery allowed here) multiplication rhombus, with blank spaces denoting 0s. Columnwise addition gives - someone please double-check my carries! - the indicated sum, matching the desired result:
[code]59649589127497217 x 5704689200685129054721:

5: 28523446003425645273605
9: + 51342202806166161492489
6: + 34228135204110774328326
4: + 22818756802740516218884
9: + 51342202806166161492489
5: + 28523446003425645273605
8: + 45637513605481032437768
9: + 51342202806166161492489
1: + 5704689200685129054721
2: + 11409378401370258109442
7: + 39932824404795903383047
4: + 22818756802740516218884
9: + 51342202806166161492489
7: + 39932824404795903383047
2: + 11409378401370258109442
1: + 5704689200685129054721
7: + 39932824404795903383047
--------------------------------------------
Sum= 340282366920938463463374607431768211457
[Nonzero Carries as noted:
11112332345456777777886775664432332 ][/code]
Whew! I need a beer. Lemma 1 may need to wait a few days. Hey, even Hercules [or "Herakles" to the OP] needed to rest between his famous labors, I'll bet.

 Batalov 2013-11-16 00:57

...and if you did it in octal, you would have been done already, because calculation of 2^128+1 in octal doesn't need a separate calculation (no Lemma 1!).
[CODE]First, prepare multiples of 3237257607274243001:
3237257607274243001 (x1)
6476537416570506002 (x2)
11736017226064751003 (x3)
15175277035361214004 (x4)
20434556644655457005 (x5)
23674036454151722006 (x6)
27133316263446165007 (x7)

Now, add them in a staircase
3237257607274243001
1152401672664431414535001 *
_________________________
3237257607274243001
20434556644655457005
11736017226064751003
20434556644655457005
15175277035361214004
3237257607274243001
15175277035361214004
3237257607274243001
11736017226064751003
15175277035361214004
15175277035361214004
23674036454151722006
23674036454151722006
6476537416570506002
27133316263446165007
23674036454151722006
3237257607274243001
15175277035361214004
6476537416570506002
20434556644655457005
3237257607274243001
3237257607274243001
_______________________________________________
4000000000000000000000000000000000000000001[/CODE]

 ewmayer 2013-11-16 01:01

There you go, invoking mysterious and highly untrustworthy "computational magic" again. :)

 literka 2013-11-16 01:28

Your posts are real eyes opener for me. In fact I learned today much more about people of this forum than in the past 3 years.
Batalov, you quoted me wrongly. You wrote 255 instead of 2^55. Someone could think that I made a mistake. Of course you cannot correct it, but be careful next time.

BTW. No matter how much you write these proofs (i.e. about F5, F6, and F7) will stay my proofs and the only thing left for you it will be to write how you can divide 2 numbers or to multiply 2 numbers.

 Batalov 2013-11-16 01:42

Of course, they will. They will stay a monument to how one can scratch one's [B]left[/B] ear not simply with the right hand, but more elegantly -- with the toe on one's right foot.

On to the same Herculean task for F8, then? Is it already in the plans?

 Batalov 2013-11-16 02:09

Here's how one "scratches left ear with the left hand".
(All you need is a pencil and one sheet of paper for up to F7 and if your handwriting is neat enough, with space to spare for the F8.)

[CODE]Lemma 5A. 641 divides 2^32+1.
Proof: 2^8 = 256.
Let's square this value two more times modulo 641, and compare to 641-1.
(256^2)%641 = 154
(154^2)%641 = 640. QED.

Lemma 6A. 274177 divides 2^64+1.
Proof: 2^16 = 65536.
Let's square this value two more times modulo 274177, and compare to 274177-1.
(65536^2)%274177= 258768.
(258768^2)%274177= 274176. QED.

Lemma 7A and so on. Same thing over and over again.[/CODE]

 literka 2013-11-16 02:18

[QUOTE=Batalov;359450]Of course, they will. They will stay a monument to how one can scratch one's [B]left[/B] ear not simply with the right hand, but more elegantly -- with the toe on one's right foot.

On to the same Herculean task for F8, then? Is it already in the plans?[/QUOTE]

I wrote "no more answers". I can make exception this time. For a while I thought I had similar proof for largest known factor of F12. You might notice that proofs for F6 and F7 are based on the same concept.
I noticed some regularities.
Since there are high degree polynomials let me introduce some abbreviations: Instead of a polynomial (-3)*x^2+4*x-5 I will write (-3)(4)(-5). Take 2 polynomials
{1){0}(-1)(1)(1)(-1)(0)(1)(0)(-1)(0)(2)(-2)(2)(-1)(1)(-1)(1)(0)(1)(0)(0)(0)(1)
and
(1)(0)(1)(-1)(0)(-1)(0)(0)(0)(1)

Product of these polynomials is
(1)(0)(0)(0)(0)(0)(0)(0)(0)(0)(0)(0)(-1)(5)(-5)(5)(-5)(5)(-5)(4)(0)(0)(0)(0)(0)(0)(0)(0)(0)(0)(0)(1)

The value of the last polynomial for the point x=4 is F6. Hence values of first 2 polynomials must be factors of F6.
What nice in this it is that last polynomial is nice looking almost symmetric polynomial.

 literka 2013-11-16 02:30

[QUOTE=Batalov;359451]Here's how one "scratches left ear with the left hand".
(All you need is a pencil and one sheet of paper for up to F7 and if your handwriting is neat enough, with space to spare for the F8.)

[CODE]Lemma 5A. 641 divides 2^32+1.
Proof: 2^8 = 256.
Let's square this value two more times modulo 641, and compare to 641-1.
(256^2)%641 = 154
(154^2)%641 = 640. QED.

Lemma 6A. 274177 divides 2^64+1.
Proof: 2^16 = 65536.
Let's square this value two more times modulo 274177, and compare to 274177-1.
(65536^2)%274177= 258768.
(258768^2)%274177= 274176. QED.

Lemma 7A and so on. Same thing over and over again.[/CODE][/QUOTE]

And you started to behave like a high school student again. Don't you see the difference between these proofs and my proofs or a proof presented by jyb (quoted from Wikipedia)?

 retina 2013-11-16 02:38

[QUOTE=ewmayer;359439]I have through exhaustive labors succeeded in verifying part 2 of my proof by dilemma. We first tabulate multiples of the larger (purported) multiplicand by 0-9: 5704689200685129054721 x ____ =
[code]
0 0
1 5704689200685129054721
2 11409378401370258109442
3 17114067602055387164163
4 22818756802740516218884
5 28523446003425645273605
6 34228135204110774328326
7 39932824404795903383047
8 45637513605481032437768
9 51342202806166161492489[/code]

And here is the resulting (no FFTs, DWTs or other suspicious 3-letter-initialism-denoted computer flummery allowed here) multiplication rhombus, with blank spaces denoting 0s. Columnwise addition gives - someone please double-check my carries! - the indicated sum, matching the desired result:
[code]59649589127497217 x 5704689200685129054721:

5: 28523446003425645273605
9: + 51342202806166161492489
6: + 34228135204110774328326
4: + 22818756802740516218884
9: + 51342202806166161492489
5: + 28523446003425645273605
8: + 45637513605481032437768
9: + 51342202806166161492489
1: + 5704689200685129054721
2: + 11409378401370258109442
7: + 39932824404795903383047
4: + 22818756802740516218884
9: + 51342202806166161492489
7: + 39932824404795903383047
2: + 11409378401370258109442
1: + 5704689200685129054721
7: + 39932824404795903383047
--------------------------------------------
Sum= 340282366920938463463374607431768211457
[Nonzero Carries as noted:
11112332345456777777886775664432332 ][/code]
Whew! I need a beer. Lemma 1 may need to wait a few days. Hey, even Hercules [or "Herakles" to the OP] needed to rest between his famous labors, I'll bet.[/QUOTE]You are so clever. You deserve a cookie young man. Ever thought about becoming a minion?

 Batalov 2013-11-16 02:57

[QUOTE=Batalov;359395]literka,

Could you please present the number of operations needed to carry on all your calculation (1) - (5), etc, compared to a simple multiplication of two factors.

It appears that to assert these:
[CODE]Several equalities will be needed:

(1) p=208648999^2+126945596^2 = 512 * q+1

(2) s = 208648999*52542249 + 126945596*31967597

(3) 126945596*52542249 - 208648999*31967597 = 1

(4) 309*q + r = 2^55

(5) r = (s div 512)+1[/CODE]
one will have to do much more ...[/QUOTE]
Write (1) through (5) for us
[QUOTE=literka;359375]...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. [/QUOTE]
Now, by your own standards: Write these calculations out for us like we did for you. Show us 208648999*52542249, show us 208648999*31967597, "prove" that 126945596*52542249 - 208648999*31967597 = 1. Don't be lazy. No computers. Then, 208648999*52542249 + 126945596*31967597, and show that this is equal to s.

Then compare to simple squaring.

 literka 2013-11-16 03:19

[QUOTE=Batalov;359461]Write (1) through (5) for us

Now, by your own standards: Write these calculations out for us like we did for you. Show us 208648999*52542249, show us 208648999*31967597, "prove" that 126945596*52542249 - 208648999*31967597 = 1. Don't be lazy. No computers. Then, 208648999*52542249 + 126945596*31967597, and show that this is equal to s.

Then compare to simple squaring.[/QUOTE]

Why should I do it for you, after you ridiculed my proofs? Read what I wrote on my webpage. These numbers are large, but very small in comparison with F7. Your "simple" squaring would give you a number comparable with F7;
My idea is such: if someone does not want to understand, leave him alone because any effort is hopeless.

 Batalov 2013-11-16 03:47

Suit yourself, because by doing this you simply admit that you failed by your own standard.

If you paid close attention, you would find that the message that I quoted was my first post; it was a question that I asked you from the very start and you [B]didn't[/B] answer; so I simply reminded you; it has nothing to do with whether you felt ridiculed or not. The second quote is also fully in context and in it, you explain the purpose of your "proof". That particular purpose is completely failed, because you cannot demonstrate (1) through (5) with less computational* effort than the straightforward computation is worth.

As to your last point, it is very important to periodically look in the mirror.

_______
*computational in broad sense, that is, down to earth: with pencil and paper.

 literka 2013-11-16 04:21

[QUOTE=Batalov;359465]Suit yourself, because by doing this you simply admit that you failed by your own standard.

If you paid close attention, you would find that the message that I quoted was my first post; it was a question that I asked you from the very start and you [B]didn't[/B] answer; so I simply reminded you; it has nothing to do with whether you felt ridiculed or not. The second quote is also fully in context and in it, you explain the purpose of your "proof". That particular purpose is completely failed, because you cannot demonstrate (1) through (5) with less computational* effort than the straightforward computation is worth.

As to your last point, it is very important to periodically look in the mirror.

_______
*computational in broad sense, that is, down to earth: with pencil and paper.[/QUOTE]

Imagine that I do not have obligation to answer all your questions, especially those, which require lot of work to answer. I still remember your unfair behavior with respect to me. You did not write posts to me, but behind my back, but I read them. Why do you think that this has nothing to do with my answering to your posts? Well, I still want to be polite and I answer your posts, but I should not do it. You have 2 choices: to accept my proofs or reject them. I do not care what you will do.

 c10ck3r 2013-11-16 05:37

[QUOTE=literka;359467]Imagine that I do not have obligation to answer all your questions, especially those, which require lot of work to answer. I still remember your unfair behavior with respect to me. You did not write posts to me, but behind my back, but I read them. Why do you think that this has nothing to do with my answering to your posts? Well, I still want to be polite and I answer your posts, but I should not do it. You have 2 choices: to accept my proofs or reject them. I do not care what you will do.[/QUOTE]
Imagine that members of this forum know "ein bissyen" of mathematics, and can recognize within seconds that your proofs are rehashing known results using more effort than would be required by any one of several methods. Throughout this thread you have disregarded the advice of computer science professionals and mathematicians as they attempted to point this out to you. Your first sentence in this quote references questions "which require lot of work to answer" (sic) seems, to members of this forum especially, as rather counter-intuitive given the amount of work you put in to prove that a known factor is indeed a known factor. There have been a number of occasions in which you have posted statements as fact and have had them disproven by [I][U][B]professionals in the field[/B][/U][/I], and yet you refuse to see this.
If you feel that you have been disrespected on this forum, you may go elsewhere, if you are so inclined. Otherwise, if you wake up and recognize that the people that have responded have been making valid points the entire time, and get the urge to learn [I][U][B]why[/B][/U][/I] your proof is, for all practical purposes, pointless, feel free to ask logical questions and to take the advice of the senior members of this forum. Also, if Robert Silverman, CRGreathouse, WBlipp, Batalov, et al. suggest reading a certain paper, [I][U][B]DO SO![/B][/U][/I] Comprehension of the sources will usually provide an understanding of why certain things work or don't work in mathematics, and how to apply them.

 LaurV 2013-11-16 06:10

You guys are geniuses! You made my day. What I say my day? You made my whole weekend!

Few brilliant quotes in this thread, which would be a pity to be lost. If you think about the context, they are even more beautiful.

[QUOTE=retina;359384][SIZE=1][COLOR=white]I considered making him do it in hexadecimal just to show that he understood how hex works but somehow that seemed a little bit too cruel even for me.[/COLOR][/SIZE][/QUOTE]
To this, I could not stop laughing, considering also the context and where is coming from, but to the next one I almost had a cardiac failure, felt down to my bottom, and is still painful, :rofl:

[QUOTE=literka;359396] <[U]to RDS[/U], (this is important!): > I read your book, but only to check the level of your mathematics.[/QUOTE]
(the words in the slicers are mine, that was an important mention to do, it would not be so funny if he would be telling it to me, for example). I imagine myself going to my sensei, provoking him to a fight, and saying that I want to test his skills. Real stuff, I am not invented anything, the man was Moroccan, 1.95 tall, 120kg, no fat, imagine Hulk Hogan young and blacker, he was studying medicine in my country in the seventies, and making some sunday money by teaching children like I was how to defend themselves. He was a wonderful person, very good in his branch (world class!) and very kind with us, but if I would go to him and do what I just said, I may not be able to post on this forum for a while, hehe...

[QUOTE=Batalov;359433]Alleged added value of the "proof": it operates only with numbers no more than 2. While direct multiplication deals with larger numbers (i.e. 3).[/QUOTE]
:w00t:

[QUOTE=literka;359464]My idea is such: if someone does not want to understand, leave him alone because any effort is hopeless.[/QUOTE]
RIGHT! BINGOOOOO! However, lot of clever people here waste precious time trying to make you understand, I don't get it why? Behaving like a log is an innate behavior.

[QUOTE=literka;359467]You did not write posts to me, but behind my back, but I read them.[/QUOTE]
(note that the posts were on a public forum, but not directly addressed to the literka thing, like I sometime write things of the type "I like/I don't like Batalov, but don't tell him", :smile:)

Let me add my wondering question markto this:
[QUOTE=Batalov;359450]On to the same Herculean task for F8, then? Is it already in the plans?[/QUOTE]
:rofl: :w00t:

------------------
Well, I have a smell for cranks. (That is because I am a kinda crank myself, and the thieves usually can smell each other, but don't tell this to anyone). I am most probably in his ignore list, after I was "treating him like he was a thing, and not a living person" when he started posting here (to which the same people in this thread jumped on my head! I bet they feel sorry now :razz:). But this literka guy (whoops! I just did it again!) is one of the dangerous type. There are many types of cranks, some are innocents, or childish, like cmd was, or genuine clowns, like don ablaze, but there also is that type of proud idiot who really believe in what he does, and believe all people around him are stupid because they don't understand what he is doing, and because they don't approve him and don't raise him on their arms. This type of guy is more dangerous if he is teaching is some elementary or gymnasium school somewhere, because he destroys the lives of many innocent children....

 jyb 2013-11-16 07:43

[/QUOTE]

Now, now. While everyone seems to agree that literka's manipulations don't have much value, they at least appear to be valid. DB clearly lacked the necessary knowledge of mathematics to even get that far. Still, he made up for it with some wonderful delusions of grandeur.

 literka 2013-11-16 08:39

[QUOTE=LaurV;359473]
(That is because I am a kinda crank myself, and the thieves usually can smell each other, but don't tell this to anyone).[/QUOTE]

This if very truth. But don't worry I won't tell it to anybody. Only the word "kinda" doesn't match.

 literka 2013-11-16 08:41

[QUOTE=jyb;359478]Now, now. While everyone seems to agree that literka's manipulations don't have much value.[/QUOTE]

Where is this information from?

 LaurV 2013-11-16 09:05

[QUOTE=literka;359483]Only the word "kinda" doesn't match.[/QUOTE]
I said [URL="http://www.thefreedictionary.com/kinda"]kinda[/URL], not [URL="http://en.wikipedia.org/wiki/Kinder_Surprise"]kinda[/URL]. :smile:

 literka 2013-11-16 09:28

[QUOTE=LaurV;359487]I said [URL="http://www.thefreedictionary.com/kinda"]kinda[/URL], not [URL="http://en.wikipedia.org/wiki/Kinder_Surprise"]kinda[/URL]. :smile:[/QUOTE]

Thanks for correction. I did not want to misquote you.

 literka 2013-11-16 09:47

[QUOTE=c10ck3r;359471]Imagine that members of this forum know "ein bissyen" of mathematics, and can recognize within seconds that your proofs are rehashing known results using more effort than would be required by any one of several methods. Throughout this thread you have disregarded the advice of computer science professionals and mathematicians as they attempted to point this out to you. Your first sentence in this quote references questions "which require lot of work to answer" (sic) seems, to members of this forum especially, as rather counter-intuitive given the amount of work you put in to prove that a known factor is indeed a known factor. There have been a number of occasions in which you have posted statements as fact and have had them disproven by [I][U][B]professionals in the field[/B][/U][/I], and yet you refuse to see this.
If you feel that you have been disrespected on this forum, you may go elsewhere, if you are so inclined. Otherwise, if you wake up and recognize that the people that have responded have been making valid points the entire time, and get the urge to learn [I][U][B]why[/B][/U][/I] your proof is, for all practical purposes, pointless, feel free to ask logical questions and to take the advice of the senior members of this forum. Also, if Robert Silverman, CRGreathouse, WBlipp, Batalov, et al. suggest reading a certain paper, [I][U][B]DO SO![/B][/U][/I] Comprehension of the sources will usually provide an understanding of why certain things work or don't work in mathematics, and how to apply them.[/QUOTE]

If you are doing this what you adviced me to do then [I][U][B]DON'T DO SO![/B][/U][/I]. Find area interesting for you and unsolved problem interesting for you and try to solve it. People will tell you that your work is worthless and this is what they will think. It is because everybody thinks that only his area of interest is worthy to pay attentions.

 cmd 2013-11-16 11:08

imo

[QUOTE=literka;359491]If you are doing this what you adviced me to do then [I][U][B]DON'T DO SO![/B][/U][/I]. Find area interesting for you and unsolved problem interesting for you and try to solve it. People will tell you that your work is worthless and this is what they will think. It is because everybody thinks that only his area of interest is worthy to pay attentions.[/QUOTE]

It [URL="http://it.emcelettronica.com/dimostrazioni-matematiche-della-non-esistenza-di-dio"]also[/URL]

:cmd:

 axn 2013-11-16 15:39

@Literka: After step 10, you should b multiplying by 512, not 256.

 LaurV 2013-11-16 16:00

What?? After all this fight, you want to say that he has a mistake in that beautiful demonstration?

(read as: did you actually wasted the time to click and read? man, you must be really free and bored! I may change my opinion about you... :razz:)

 literka 2013-11-16 16:19

[QUOTE=axn;359515]@Literka: After step 10, you should b multiplying by 512, not 256.[/QUOTE]

Thank you. I corrected. If you agree I can include short note at the end of a page of the form "I am grateful to ..... for reading and correcting text".
In the case you agree, I would need your name.

 BudgieJane 2013-11-16 17:21

I am amazed that so much has been written in this thread about the factorization of F7. As far as I am concerned you pass the number into YAFU, wait a short while, and pick up the factors out the other end. End of story, pass on to the next number.

Since you will have done this one a few years ago, with all the others you will have done in the meantime you should be looking at F77 now, or even F777, and certainly not F7.

 literka 2013-11-16 17:32

[QUOTE=BudgieJane;359530]I am amazed that so much has been written in this thread about the factorization of F7. As far as I am concerned you pass the number into YAFU, wait a short while, and pick up the factors out the other end. End of story, pass on to the next number.
[/QUOTE]

Yes, it is a wonderful idea. I waited less than 1 sec. for a result.

[QUOTE=BudgieJane;359530]
Since you will have done this one a few years ago, with all the others you will have done in the meantime you should be looking at F77 now, or even F777, and certainly not F7.[/QUOTE]

I don't like number 7. I would better do F88.

 c10ck3r 2013-11-16 19:27

[QUOTE=literka;359534]
I don't like number 7. I would better do F88.[/QUOTE]

F88 would take too long to write out manually. Might I suggest F20 instead? Its a nice, round number, and much smaller :)
If you make any usable* progress, I will pay your website's hosting costs for a year.

*Usable progress will be determined and prizes awarded at the discretion of the challenge creator.

 Batalov 2013-11-16 20:03

[QUOTE=literka;359518]Thank you. I corrected. If you agree I can include short note at the end of a page of the form "I am grateful to ..... for reading and correcting text".
In the case you agree, I would need your name.[/QUOTE]
His name is Anand Nair and if you will fail to mention his contribution, your page will be a forgery.
[QUOTE=literka;359446]BTW. No matter how much you write these proofs (i.e. about F5, F6, and F7) [SIZE=4]will stay my proofs [/SIZE][/QUOTE]
Even this is no longer true. You didn't even [I]have[/I] a proof until Anand Nair corrected you.

 literka 2013-11-16 20:24

[QUOTE=Batalov;359545]His name is Anand Nair and if you will fail to mention his contribution, your page will be a forgery.
[/QUOTE]

I need agreement from Axn, not from you.

[QUOTE=Batalov;359545]Even this is no longer true. You didn't even [I]have[/I] a proof until Anand Nair corrected you.[/QUOTE]

So, the result now is Anand's result? I thought it was my result for life. Oh no, I will start to cry very soon.

 jyb 2013-11-16 22:41

[QUOTE=literka;359484]
[QUOTE=jyb;359478]Now, now. While everyone seems to agree that literka's manipulations don't have much value....[/QUOTE]
Where is this information from?[/QUOTE]

Indeed, perhaps I abused the word "everyone". You, at least, are exempt from this group. Otherwise I will cite as evidence that several people have stated or implied that this work is without value, and so far nobody has presented a contrary opinion.

Still, to give you the benefit of the doubt, can you explain what value this work does have? I.e. what is interesting about your work? Not the result, clearly, since I think everyone was quite convinced that 59649589127497217 is a factor of F7; so it must be the method. What makes your method worth studying? What is there to learn from it?

Note that I am not asking these questions in a judgmental, rhetorical way (i.e. to imply that the answer is "nothing"). I am genuinely curious as to what value you think this adds to mathematics.

 literka 2013-11-16 23:23

[QUOTE=jyb;359559]Indeed, perhaps I abused the word "everyone". You, at least, are exempt from this group. Otherwise I will cite as evidence that several people have stated or implied that this work is without value, and so far nobody has presented a contrary opinion.

Still, to give you the benefit of the doubt, can you explain what value this work does have? I.e. what is interesting about your work? Not the result, clearly, since I think everyone was quite convinced that 59649589127497217 is a factor of F7; so it must be the method. What makes your method worth studying? What is there to learn from it?

Note that I am not asking these questions in a judgmental, rhetorical way (i.e. to imply that the answer is "nothing"). I am genuinely curious as to what value you think this adds to mathematics.[/QUOTE]

You asked me a philosophical question. That is why I will not answer it. There were always such questions i.e. when Four Colors Th. was proved there were such questions, the same about Bieberbach Th, and even Fermat's Th. These are hard questions to answer, especially to people, who don't know mathematics or to the people like you, who are convinced that something is worthless.
Anyway, don't ask me such questions, because I am not a philosopher. I don't mind if you have your own opinion, and even I will appreciate it.

 R.D. Silverman 2013-11-16 23:58

[QUOTE=literka;359560]You asked me a philosophical question. That is why I will not answer it.
[/QUOTE]

any mathematical argument. It is NOT "philosophical"

You, in turn replied in typical crank fashion by evasion and refusal to

I think the reason why you refuse to answer is that you know that

Every time you open your mouth you come across like an ignorant
and arrogant ass. Ignorance and arrogance is quite a combination.

 literka 2013-11-17 00:04

[QUOTE=R.D. Silverman;359562]The question was simple, direct, and can be properly asked about
any mathematical argument. It is NOT "philosophical"

You, in turn replied in typical crank fashion by evasion and refusal to

I think the reason why you refuse to answer is that you know that

Every time you open your mouth you come across like an ignorant
and arrogant ass. Ignorance and arrogance is quite a combination.[/QUOTE]

Stop provoking me. Because of you I am in "Misc.". If you think that a supermod will have a reason to intervene, then I will answer - Not this time my dear.

 chalsall 2013-11-17 00:18

[QUOTE=literka;359563]Stop provoking me. Because of you I am in "Misc.". If you think that a supermod will have a reason to intervene, then I will answer - Not this time my dear.[/QUOTE]

Just to be very clear, the "supermods" always enjoy a good, fair and honest fight.

Usually this is just a verbal debate about ideas, but sometimes it involves atoms moving at high speed....

 literka 2013-11-17 00:25

[QUOTE=chalsall;359566]Just to be very clear, the "supermods" always enjoy a good, fair and honest fight.

Usually this is just a verbal debate about ideas, but sometimes it involves atoms moving at high speed....[/QUOTE]

Is this really a fair debate, when one person calls another a crank? I did not use such a word, but I was moved to "Misc.". I don't mind, but I don't want any trouble.

 chalsall 2013-11-17 00:30

[QUOTE=literka;359567]Is this really a fair debate, when one person calls another a crank? I did not use such a word, but I was moved to "Misc.". I don't mind, but I don't want any trouble.[/QUOTE]

Learn how to debate, grasshopper...

State what (and only what) you are comfortable defending.

You don't need to bat at every ball. Read: Choose your battles.

 literka 2013-11-17 00:43

[QUOTE=chalsall;359568]Learn how to debate, grasshopper...

State what (and only what) you are comfortable defending.

You don't need to bat at every ball. Read: Choose your battles.[/QUOTE]

Thanks for your lesson. I don't want to defend anything. I just don't want to be called crank or grasshopper.

 chalsall 2013-11-17 00:55

[QUOTE=literka;359569]Thanks for your lesson. I don't want to defend anything. I just don't want to be called crank or grasshopper.[/QUOTE]

Be comfortable being called anything.

 literka 2013-11-17 00:58

[QUOTE=chalsall;359571]Be comfortable being called anything.[/QUOTE]

OK. I will. Only that I will not answer to any abusive post.

 chalsall 2013-11-17 01:09

[QUOTE=literka;359572]OK. I will. Only that I will not answer to any abusive post.[/QUOTE]

That's perfectly fine.

Be comfortable in your own skin.

Be comfortable where you find yourself, and where you put yourself.

 Batalov 2013-11-17 02:30

[QUOTE=BudgieJane;359530]I am amazed that so much has been written in this thread about the factorization of F7. Since you will have done this one a few years ago, with all the others you will have done in the meantime you should be looking at F77 now, or even F777, and certainly not F7.[/QUOTE]
In fact, far beyond that. Some of us already found factors for F1132, F9447, F17748, and F106432. And that's no joke. The factors are too large for the margins of this thread to contain. You can find them elsewhere. Some others found even larger factors (longer than 800,000 digits).

Certainly, some people will never believe that 30967*2^106436+1 divides 2[SUP]2[SUP]106432[/SUP][/SUP]+1. How can they? [I]There were computers involved![/I] Surely, it is a lie, isn't it?
-- No, it is not a lie, "and stop calling me Shirley". Furthermore, wrap you head around this: how can you be sure that 2[SUP]57,885,161[/SUP]-1 is prime? You can't, can you!

I hate to appeal to authority (in this case an authority of actually having done something before talking). But some people can only understand a direct illustration.

 c10ck3r 2013-11-17 04:18

The preceding was a paid advertisement for PFGW. The views expressed are not necessarily those of the management and staff of this station.

 jyb 2013-11-17 05:31

[QUOTE=literka;359560]These are hard questions to answer, especially to people, who don't know mathematics or to the people like you, who are convinced that something is worthless.[/QUOTE]

Did you see the part of my post where I indicated that I was not trying to imply anything with my questions? I really was trying to reserve judgment. When I asked the questions, I was not fully convinced that your work was worthless. But your response has sure moved me closer to that conclusion.

 Batalov 2013-11-17 06:56

[QUOTE=c10ck3r;359583]The preceding was a paid advertisement for PFGW. The views expressed are not necessarily those of the management and staff of this station.[/QUOTE]
You forgot Paul Jobling, Jim Fougeron and Geoffrey Walter Reynolds. They all paid for it, too. And one George Woltman definitely chipped in a few drops of sweat, blood or something.

 literka 2013-11-17 08:34

[QUOTE=jyb;359588]Did you see the part of my post where I indicated that I was not trying to imply anything with my questions? I really was trying to reserve judgment. When I asked the questions, I was not fully convinced that your work was worthless. But your response has sure moved me closer to that conclusion.[/QUOTE]

Two people A and B met. Mr, A has a house in mountains with no electricity and road leading to this house. Mr. A says "I have a valuable house". Mr. B says "this house is worthless. I would never live in this house".
The discussion who is right may lead only to a quarrel, since both are right and both are wrong in the same time.
As I said before: You may have your own opinion. I will respect your opinion, but don't press me any further, because I am convinced about one - the discussion would be worthless.

 BudgieJane 2013-11-17 09:29

[QUOTE=literka;359569]I just don't want to be called crank ...[/QUOTE]

The crank is one of humankind’s most useful inventions. It is defined as a right-angled arm attached to a rotating shaft that converts circular motion into reciprocal motion or vice versa.

Cranks are commonly found on treadle sewing machines, pencil sharpeners, fishing reels and internal combustion engines. Simple cranks were used by the Romans in hand mills and by the Greeks in Archimedes screws 2000 years ago.

Just remember that cranks make the world go around.

How are you getting on with F88?

 literka 2013-11-17 10:33

[QUOTE=BudgieJane;359601]The crank is one of humankind’s most useful inventions. It is defined as a right-angled arm attached to a rotating shaft that converts circular motion into reciprocal motion or vice versa.

Cranks are commonly found on treadle sewing machines, pencil sharpeners, fishing reels and internal combustion engines. Simple cranks were used by the Romans in hand mills and by the Greeks in Archimedes screws 2000 years ago.

Just remember that cranks make the world go around.
[/QUOTE]

Still I don't want to be a crank. The most I dislike it is this "reciprocal motion".

[QUOTE=BudgieJane;359601]
How are you getting on with F88?[/QUOTE]

If I knew I would write another page. A new concept is required.

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