20040412, 18:58  #1 
Banned
"Luigi"
Aug 2002
Team Italia
4,793 Posts 
62digit 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 62digit prime (about 204.62 bit) obtained with trialfactoring software. Geee, it's fun! Luigi 
20060322, 23:58  #2 
6809 > 6502
"""""""""""""""""""
Aug 2003
101×103 Posts
2^{3}·1,151 Posts 
Is that still the record?

20060323, 01:18  #3  
Nov 2003
2^{2}·5·373 Posts 
Quote:
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 2^6831, 2^7271, and 2^8111, for example. 

20060323, 06:11  #4 
6809 > 6502
"""""""""""""""""""
Aug 2003
101×103 Posts
10001111111000_{2} Posts 
Testing an app sometimes yields a fun answer.

20060323, 13:06  #5  
Nov 2003
2^{2}·5·373 Posts 
Quote:
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. 

20060324, 03:42  #6 
Sep 2002
11×71 Posts 
Dr. Silverman, you still just don't know how to let people have their fun without negatively commenting.

20060324, 10:19  #7  
Nov 2003
2^{2}×5×373 Posts 
Quote:
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. 

20060324, 12:43  #8  
Jul 2004
Potsdam, Germany
3·277 Posts 
Quote:
Quote:
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... 

20060324, 19:39  #9  
Bemusing Prompter
"Danny"
Dec 2002
California
100100110001_{2} Posts 
Quote:


20060324, 22:26  #10  
6809 > 6502
"""""""""""""""""""
Aug 2003
101×103 Posts
2^{3}×1,151 Posts 
Quote:
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 nonfactoring related posts. 

20060324, 23:16  #11 
Sep 2004
2830_{10} Posts 
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 20060324 at 23:20 
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