Complete Factorization???

Khemikal796 · 2005-04-13, 04:27

Could someone provide me with a quick walkthrough of which programs to use, hopefully just Prime95, and which settings and such I would use if I wanted to completely factor a given exponent. Recently found a factor to an exponent that looked funny, and I would like to see if I cant completely factor this puppy. I know itll take ages, and I dont care. I just want to do it

. Thanks in advanced. If you need any more info please leave a reply and Ill see what I can do to answer.

Wacky · 2005-04-13, 11:28

Quote:

Originally Posted by Khemikal796

Could someone provide me with a quick walkthrough of which programs to use, hopefully just Prime95, and which settings and such I would use if I wanted to completely factor a given exponent. Recently found a factor to an exponent that looked funny, and I would like to see if I cant completely factor this puppy. I know itll take ages, and I dont care. I just want to do it

. Thanks in advanced. If you need any more info please leave a reply and Ill see what I can do to answer.

Guessing at the size of the number that you might be considering, the chances are "you can not do it". Not only that, but the best mathematicians, with the largest computers available today, could not do it within your lifetime unless there is a breakthrough in factoring algorithms.

Except for some special cases, the best algorithm presently known has not yet factored a Mersenne number of 1000 bits. To do even that, will require programs that have yet to be written.

Tell us the particular number and we can give you a more definite answer as to what you might do to obtain some additional factors.

Khemikal796 · 2005-04-13, 17:06

Well thanks for not answering the question at hand. I will not tell you any more about number than the exponent is not small. Something as simple as just running the factor to such and such a bit would have been good if you dont think its possible. Obviously Im not getting the dreamers and thinkers attentions with this thread. Next please!

R.D. Silverman · 2005-04-13, 17:51

Quote:

Originally Posted by Khemikal796

Well thanks for not answering the question at hand. I will not tell you any more about number than the exponent is not small. Something as simple as just running the factor to such and such a bit would have been good if you dont think its possible. Obviously Im not getting the dreamers and thinkers attentions with this thread. Next please!

Typical crank response.

Someone with little knowledge asks a vague question.

Someone with superior knowledge guesses what was meant and informs
the crank that success is unlikely.

The crank then replies with sarcasm, a refusal to divulge the information
that would allow a more detailed answer, and a gratuitous insult at the end.

Can you say "juvenile"?????

Finally, the phrase "such and such a bit" is not mathematics. If you want to
discuss mathematics, then I suggest you use standard terminology.

akruppa · 2005-04-13, 17:59

Khemikal796, Wacky's answer was exactly right. Your reaction was inappropriate.

Alex

VJS · 2005-04-13, 18:26

Here is probably the answer your looking for.

Depending upon the exponent it will probably be impossible for you to completely factor the number by yourself.

In layman's terms...

If your n i.e. k.2^n-1 is larger than 300 you probably won't be able to totally factor it yourself in a reasonable time frame, you might if you get very very lucky.

If your n is greater than 1000 near impossible, if it's one of the gimps numbers i.e. n=32M or n=32,000,000 ... if everyone in the world started now we probably wouldn't be able to finish it before we all die.

When people ask for the exponent they need to know roughly what the number is so they can direct you. Can you tell us that much? If it's n=323 then say it's between 300-400, if it's 97 say it's less than 100, etc...

Your best place to start is...

http://www.alpertron.com.ar/ECM.HTM

If your number is to large to factor here give up now, if it's not them there is a possibility and better faster programs etc.

Khemikal796 · 2005-04-13, 20:09

I simply asked how to go about TRYING to do it. I mentioned that it was very likely that it would take a very long time. I do not like being told that I can not factor a number when I can, or atleast attempt to. It is possible to factor any number into its primes. Thus I can factor the number I want. A simply point in the right direction was all I asked for. As for the juvenille remark, just because I have not proven my worth in the math forums infront of you people does not make me any less of a person in the community than you Silverman. Yes I realize I probably have not the exposure to the math that you have, yet I am doing my best to learn. You calling me a 'juvenille' is just as useless and uncalled for as someone calling someone else a 'n00b' in a game. It gets you nowhere. Im here to learn, and thats what I will do regardless. If you guys are going to criticize me thats ok. I simply want to learn. If you feel that my response was inappropriate, then maybe the appropriate response from some of the more senior members would have been a private message to me saying what I should have done so I could have edited, or changed my post. Thanks VJS for the link. Ill check it out and see if I can make sense of it, and hope that it will do what Im hoping it will.

Uncwilly · 2005-04-13, 20:21

If your number is a mersenne that is ~7million digits long and you have found a 60 digit factor, that leaves a co-factor of ~7million digits long. The co-factor may be prime (and not able to be L-L tested or otherwise proven to be time), it may be a standard composite (however since you have found the lowest factor, all the remaining will be larger and vastly harder to find), or it may be the product of 2 very large primes (possibly even a sqaure of a 3.5million digit number). All of these tend to be beyond all available tools for a number of that size.

wblipp · 2005-04-13, 21:06

Quote:

Originally Posted by Khemikal796

Thus I can factor the number I want.

Sigh.

This just isn't true.

If your number is a recent GIMPS number, then it is not possible to completely factor this number using existing hardware and existing algorithms within the life of the universe. It's like you want advice on how to jump high enough to touch the moon.

If your number is much smaller, there might be some hope - the Cunningham Project reqularly completes factorization of small Mersenne numbers, and ElevenSmooth has been lucky enough to complete a few. But people need to know the approximate size to give you any useful advice.

VJS · 2005-04-14, 15:17

Quote:

Originally Posted by wblipp

Sigh.
If your number is much smaller, there might be some hope - the Cunningham Project reqularly completes factorization of small Mersenne numbers, and ElevenSmooth has been lucky enough to complete a few. But people need to know the approximate size to give you any useful advice.

A very good answer worthy of a quote.

Khemikal796 please tell us the relative size of the number and the form this is not giving up much information. It would basically be the same as saying I burried my fortune and I need help finding it what tools do I use. You could also add, it's gold and I burried it in a forest in north england people would never find it.

Is your number of the form

2^n-1
2^n+1
k^n-1
k^n+1
k.2^n-1
k.2^n+1

And what (roughly) is the size of the n.

There are much better faster programs out there than I mentioned, we could also help you to use that program.

Recently I fully factored a number where n=7322 it only took me two days b/c I was very very very lucky. One factor was small the remaining portion was prime.

Also one should always ignore trolls in forums, and let me break this to you lightly you are a nOOb, let me break this to everyone else they were once nOOb's as well. Were not trying to trick you just help you or at least point you in the right direction.

Khemikal796 · 2005-04-14, 20:51

The number is a Mersenne number. Ive already found a 62 bit factor. The exponent is a few thousand time bigger than the n you factored. I do realize that like you guys have said multiple times over, that I most likely wont be able to completely factor this number in my lifetime. If I manage a few factors out of it that would be very cool and I would be a happy camper. I would like to attempt it just because I can. Wacky mentioned ECMing would be a good approach, yet I do not know the ideals behind which curves and such to use for respective exponent, or how many to run for each given range. Thus Im fairly lost in using this method.

2005-04-13, 04:27	#1
Khemikal796 Feb 2003 45₈ Posts	Complete Factorization??? Could someone provide me with a quick walkthrough of which programs to use, hopefully just Prime95, and which settings and such I would use if I wanted to completely factor a given exponent. Recently found a factor to an exponent that looked funny, and I would like to see if I cant completely factor this puppy. I know itll take ages, and I dont care. I just want to do it . Thanks in advanced. If you need any more info please leave a reply and Ill see what I can do to answer.

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2005-04-13, 17:06	#3
Khemikal796 Feb 2003 37 Posts	Well thanks for not answering the question at hand. I will not tell you any more about number than the exponent is not small. Something as simple as just running the factor to such and such a bit would have been good if you dont think its possible. Obviously Im not getting the dreamers and thinkers attentions with this thread. Next please!

2005-04-13, 17:59	#5
akruppa "Nancy" Aug 2002 Alexandria 2,467 Posts	Khemikal796, Wacky's answer was exactly right. Your reaction was inappropriate. Alex

2005-04-13, 18:26	#6
VJS Dec 2004 13·23 Posts	Here is probably the answer your looking for. Depending upon the exponent it will probably be impossible for you to completely factor the number by yourself. In layman's terms... If your n i.e. k.2^n-1 is larger than 300 you probably won't be able to totally factor it yourself in a reasonable time frame, you might if you get very very lucky. If your n is greater than 1000 near impossible, if it's one of the gimps numbers i.e. n=32M or n=32,000,000 ... if everyone in the world started now we probably wouldn't be able to finish it before we all die. When people ask for the exponent they need to know roughly what the number is so they can direct you. Can you tell us that much? If it's n=323 then say it's between 300-400, if it's 97 say it's less than 100, etc... Your best place to start is... http://www.alpertron.com.ar/ECM.HTM If your number is to large to factor here give up now, if it's not them there is a possibility and better faster programs etc.

2005-04-13, 20:09	#7
Khemikal796 Feb 2003 37 Posts	I simply asked how to go about TRYING to do it. I mentioned that it was very likely that it would take a very long time. I do not like being told that I can not factor a number when I can, or atleast attempt to. It is possible to factor any number into its primes. Thus I can factor the number I want. A simply point in the right direction was all I asked for. As for the juvenille remark, just because I have not proven my worth in the math forums infront of you people does not make me any less of a person in the community than you Silverman. Yes I realize I probably have not the exposure to the math that you have, yet I am doing my best to learn. You calling me a 'juvenille' is just as useless and uncalled for as someone calling someone else a 'n00b' in a game. It gets you nowhere. Im here to learn, and thats what I will do regardless. If you guys are going to criticize me thats ok. I simply want to learn. If you feel that my response was inappropriate, then maybe the appropriate response from some of the more senior members would have been a private message to me saying what I should have done so I could have edited, or changed my post. Thanks VJS for the link. Ill check it out and see if I can make sense of it, and hope that it will do what Im hoping it will.

2005-04-13, 20:21	#8
Uncwilly 6809 > 6502 """"""""""""""""""" Aug 2003 101×103 Posts 2×47×113 Posts	If your number is a mersenne that is ~7million digits long and you have found a 60 digit factor, that leaves a co-factor of ~7million digits long. The co-factor may be prime (and not able to be L-L tested or otherwise proven to be time), it may be a standard composite (however since you have found the lowest factor, all the remaining will be larger and vastly harder to find), or it may be the product of 2 very large primes (possibly even a sqaure of a 3.5million digit number). All of these tend to be beyond all available tools for a number of that size.

2005-04-14, 20:51	#11
Khemikal796 Feb 2003 37 Posts	The number is a Mersenne number. Ive already found a 62 bit factor. The exponent is a few thousand time bigger than the n you factored. I do realize that like you guys have said multiple times over, that I most likely wont be able to completely factor this number in my lifetime. If I manage a few factors out of it that would be very cool and I would be a happy camper. I would like to attempt it just because I can. Wacky mentioned ECMing would be a good approach, yet I do not know the ideals behind which curves and such to use for respective exponent, or how many to run for each given range. Thus Im fairly lost in using this method.