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Old 2004-04-12, 18:58   #1
ET_
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Default 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!

Luigi
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Old 2006-03-22, 23:58   #2
Uncwilly
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Is that still the record?
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Old 2006-03-23, 01:18   #3
R.D. Silverman
 
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Quote:
Originally Posted by 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!

Luigi
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.
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Old 2006-03-23, 06:11   #4
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Testing an app sometimes yields a fun answer.
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Old 2006-03-23, 13:06   #5
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Quote:
Originally Posted by Uncwilly
Testing an app sometimes yields a fun answer.
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.
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Old 2006-03-24, 03:42   #6
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Dr. Silverman, you still just don't know how to let people have their fun without negatively commenting.
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Old 2006-03-24, 10:19   #7
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Quote:
Originally Posted by Jwb52z
Dr. Silverman, you still just don't know how to let people have their fun without negatively commenting.
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.
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Old 2006-03-24, 12:43   #8
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Quote:
Originally Posted by R.D. Silverman
As I said, writing the app merits respect.
Spending milliseconds of computer time to find a trivial result does not.
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.
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...
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Old 2006-03-24, 19:39   #9
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Quote:
Originally Posted by Mystwalker
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.

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...
Pun intended?
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Old 2006-03-24, 22:26   #10
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Quote:
Originally Posted by R.D. Silverman
I am not the one prattling and spewing hyperbole about "beautiful result" over something that is trivial....
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.
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Old 2006-03-24, 23:16   #11
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Why don't you guys ignore R.D. Silverman?

I don't know what a hell is the administrator doing but R.D. Silverman 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 R.D. Silverman be banned? Yes or No.
I think I know the answer.

Last fiddled with by em99010pepe on 2006-03-24 at 23:20
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