Number 59649589127497217 is a factor of Fermat number F7

[retina]

Originally Posted by Mini-Geek

It's far easier to trust a computer.

Sure. If the hackers/NSA/GCHQ haven't gotten their codez into it.

Originally Posted by Mini-Geek

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.

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.

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.

[R.D. Silverman]

Originally Posted by literka

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.

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]

Originally Posted by Mini-Geek

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?).

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]

Originally Posted by R.D. Silverman

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.

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]

Originally Posted by literka

At least I supported my statement with some facts.

False. You presented no facts.

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

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

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.

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]

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:

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

one will have to do much more than to simply assert

59649589127497217 *
5704689200685129054721
= 340282366920938463463374607431768211457 
= 2^128+1

And even less work in octal (with an octal multiplication table at your side)

2^128+1 = 4000000000000000000000000000000000000000001
(note: this equality you will have for free!) 
and then

3237257607274243001
*
1152401672664431414535001 
= 
4000000000000000000000000000000000000000001

[literka]

Originally Posted by R.D. Silverman

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. .

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]

Originally Posted by literka

I did not see anything you did in mathematics

Google is your friend.

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]

Originally Posted by Batalov

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:

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

one will have to do much more than to simply assert

59649589127497217 *
5704689200685129054721
= 340282366920938463463374607431768211457 
= 2^128+1

And even less work in octal (with an octal multiplication table at your side)

2^128+1 = 4000000000000000000000000000000000000000001
(note: this equality you will have for free!) 
and then

3237257607274243001
*
1152401672664431414535001 
= 
4000000000000000000000000000000000000000001

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]

Originally Posted by wblipp

Google is your friend.

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.

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]

Originally Posted by literka

Page of Wikipedia is not about F5 but about all Fermat numbers.

Exactly.

Originally Posted by literka

Still, they thought that it is worthy to include proof about the number 641.

What proof? What are you talking about?