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-   -   62-digit prime factor of a Mersenne number (https://www.mersenneforum.org/showthread.php?t=2346)

ET_ 2004-04-12 18:58

62-digit prime factor of a Mersenne number
 
Playing with my applet, i found out this beautiful result:

M1000000000000000000000000000000000000000000000000000000001059 has a factor: 40000000000000000000000000000000000000000000000000000000042361

The factor being a 62-digit prime (about 204.62 bit) obtained with trial-factoring software.

Geee, it's fun! :bounce:

Luigi

Uncwilly 2006-03-22 23:58

Is that still the record?

R.D. Silverman 2006-03-23 01:18

[QUOTE=ET_]Playing with my applet, i found out this beautiful result:

M1000000000000000000000000000000000000000000000000000000001059 has a factor: 40000000000000000000000000000000000000000000000000000000042361

The factor being a 62-digit prime (about 204.62 bit) obtained with trial-factoring software.

Geee, it's fun! :bounce:

Luigi[/QUOTE]

If people would only learn a little mathematics, this kind of silliness would
stop. I keep telling people: do a little math BEFORE computing. But noone
seems to listen. I speculate that this is because math is hard, computing is easy, and participants herein can't be bothered doing anything that is *hard*.

The reward that comes from doing something HARD is a lot greater than
doing something EASY.

It is a *TOTALLY trivial* matter to find very large factors of very very large
Mersenne numbers. I will give a hint: Let p be a prime that is 3
mod 4 such that 2p+1 is also prime. Now consider the Mersenne
number M_p. Think 'quadratic reciprocity' and 'Euler's Theorem'.

Note that this 'factor' is discovered without any "trial division" at all.

What *would* be impressive would be finding a 62 digit factor of a
relatively small Mersenne number. (say) p < 2000.

And factors larger than 62 digits of Mersenne numbers have been found.
Quite a few. Look at 2^683-1, 2^727-1, and 2^811-1, for example.

Uncwilly 2006-03-23 06:11

[B]Testing[/B] an app sometimes yields a fun answer.

R.D. Silverman 2006-03-23 13:06

[QUOTE=Uncwilly][B]Testing[/B] an app sometimes yields a fun answer.[/QUOTE]

Indeed. There is considerable merit in writing, debugging and testing a
computational app. Such work merits respect.

But the discussion should be about the app, and not some imagined
'record'. Especially since a few minutes googling would reveal that it
isn't a record at all.

Jwb52z 2006-03-24 03:42

Dr. Silverman, you still just don't know how to let people have their fun without negatively commenting.

R.D. Silverman 2006-03-24 10:19

[QUOTE=Jwb52z]Dr. Silverman, you still just don't know how to let people have their fun without negatively commenting.[/QUOTE]

I am not the one prattling and spewing hyperbole about "beautiful result"
over something that is trivial. I am not the one speculating about
"records" in a situation where any record that might be set is trivially
broken with a small effort.

I do not go into forums where I am ignorant and spew nonsense.

As I said, writing the app merits respect.

Spending milliseconds of computer time to find a trivial result does not.

We see here yet another instamce of the "instant gratification" generation
in action.

Mystwalker 2006-03-24 12:43

[QUOTE=R.D. Silverman]As I said, writing the app merits respect.
Spending milliseconds of computer time to find a trivial result does not.[/quote]

I think this is a prime example of diverging opinions. Some people think like that, others don't. I hope no one imagines that his/her own opinion is right, and all others are wrong. I would put this under "arrogance", frankly speaking.

[quote]We see here yet another instamce of the "instant gratification" generation in action.[/QUOTE]

It all depends on the perspective. From a OS programmer's point of view, you also just take what is there already. I'm quite certain that there are OS programmers who think of such "trivial" applications (no sophisticated device handlers, no low-level storage accesses, no extensive communication channels) likewise...

Personally, I typically use what is already there (and e.g. build on top of it). And I don't think that this should be called "instant gratification", only because I efficiently use existing ressources...

ixfd64 2006-03-24 19:39

[QUOTE=Mystwalker]I think this is a [b]prime[/b] example of diverging opinions. Some people think like that, others don't. I hope no one imagines that his/her own opinion is right, and all others are wrong. I would put this under "arrogance", frankly speaking.

It all depends on the perspective. From a OS programmer's point of view, you also just take what is there already. I'm quite certain that there are OS programmers who think of such "trivial" applications (no sophisticated device handlers, no low-level storage accesses, no extensive communication channels) likewise...

Personally, I typically use what is already there (and e.g. build on top of it). And I don't think that this should be called "instant gratification", only because I efficiently use existing ressources...[/QUOTE]

Pun intended?

Uncwilly 2006-03-24 22:26

[QUOTE=R.D. Silverman]I am not the one prattling and spewing hyperbole about "beautiful result" over something that is trivial....[/QUOTE]You appear to not understand the intent of my intial response. I was not asking if that was a "world record". I was asking ET if that was his current record for his factoring app. Context. I have worked with ET on his projects, thus a personal interaction. The result is a beauty in that it shows that his app works.

I did not "go into forums where I am ignorant and spew nonsense". I was asking the original poster a question about his app. I am not wholly ignornant of factoring. Since the date of the post ET has upgrade his app. I wonder if he has tested it with larger numbers.

You stated: "We see here yet another instamce of the "instant gratification" generation in action."
I am unaware of the word "instamce".
Are you claiming that ET is or I am part of that "generation"? Him for sharing a small point of joy? Or me for asking a question?

Since this is a factoring forum, this will be my last response to non-factoring related posts.

em99010pepe 2006-03-24 23:16

Why don't you guys ignore [URL="http://www.mersenneforum.org/member.php?u=1442"]R.D. Silverman[/URL]?

I don't know what a hell is the administrator doing but [URL="http://www.mersenneforum.org/member.php?u=1442"]R.D. Silverman[/URL] is giving a bad imagine of the mersenne forum.

I bet most of people feel afraid to ask something because of the reaction of that person.

Someday I will start a poll about him, something like:

Should [URL="http://www.mersenneforum.org/member.php?u=1442"]R.D. Silverman[/URL] be banned? Yes or No.
I think I know the answer.


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