Didn't even find a useless factor of an uninteresting number! Take that! - Page 10

storflyt32 · 2016-01-20, 04:17

Thanks for the suggestion, wblipp.

But if I am not wrong, GCD will not be able to return the correct answer when one of the numbers are composite.

Therefore I am not getting this working right now.

Anyway, congratulations to you for the new Mersenne prime number.

This is a great, or really magnificent find!

You possibly already know that I happen not to be doing the same thing and you certainly already know why.

If you do not know, I happened to get my knowledge about numbers by entering the wrong door, namely by means of +1 rather than -1.

Is it possible to compare the total number of factors, or possibly prime numbers when looking at Mersenne numbers and factors versus Fermat factors?

If being slightly terse in my language, there is no such thing as a Fermat prime, only Fermat factors and prime numbers which rather are being designated Genefer primes.

In fact, a given number which could possibly be regarded as being a Fermat number still may be composite, because there remains at least one factor or perhaps more in order to have such a number fully factorized.

At least one such number lies on my disc. It is a P245 and if added to the Factor Database makes the number it is one of the factors of fully factored.

Other similar numbers lies on a disc on my shelf which is not bootable.

It should be easy to understand that I am not readily able to factorize 100 down to 11.

In the same way, neither 5 * 17 or 2 * 7 * 7 are not able to return 97.

Also you certainly know that it could take quite a long time when the number is being large.

There you have most of the problem in a nutshell.

Compare with this number, for example, namely 7810^128 + 1

http://factordb.com/index.php?id=1100000000622746569

http://factordb.com/index.php?id=1100000000487350801

Because you are doing what you are supposed to be doing, you will not be able to give me any advice here.

The C499 does not divide with the P215, by the way.

For every answer or result being found, there remains yet another question to be solved.

Dubslow · 2016-01-20, 07:13

Quote:

Originally Posted by storflyt32

Thanks for the suggestion, wblipp.

But if I am not wrong, GCD will not be able to return the correct answer when one of the numbers are composite.

You are very wrong. Very very very wrong.

BudgieJane · 2016-01-20, 13:48

Quote:

Originally Posted by wblipp

GCD

Quote:

Originally Posted by storflyt32

Thanks for the suggestion, wblipp.

But if I am not wrong, GCD will not be able to return the correct answer when one of the numbers are composite.

Therefore I am not getting this working right now.

Do you actually know what you are talking about? GCD is an acronym for Greatest Common Divisor, so if a factor of one number is a factor of another, the GCD of those numbers will be greater than 1, and both numbers will be composite. The GCD will be 1 when the numbers are relatively prime. So if one of the numbers is prime and the other composite, as long as the prime does not divide the composite number the GCD will be 1.

I learned all of this when I was in year 6 at school, about 60 years ago. Did you ever do this stuff in school? If not, your schooling was very bad, and you should complain about it.

LaurV · 2016-01-20, 13:53

Don't click reply to this bot's messages. Don't reply to him and don't post anymore in this thread. This thread is specially for him to talk alone. Otherwise he has notification set so it will get notified when someone reply, and will continue to troll the forum forever.

storflyt32 · 2016-01-21, 03:50

http://factordb.com/index.php?id=1100000000816954288

http://factordb.com/index.php?id=1100000000816944358

http://factordb.com/index.php?id=1100000000816968957

Here is an example when it comes to the use of GCD.

The third link is the dividing difference between the two first results.

Edit: Perhaps a slight misunderstanding here.

With my computer, I am not able to only factorize (or at least trying) one single number, but possibly be looking at one or more number, or sets of numbers against another number, or set of numbers.

Possibly this may be the reason for the slight confusion here.

You probably will not be able to factorize the C165 from what you already have, even when using GCD.

storflyt32 · 2016-01-21, 17:18

http://factordb.com/index.php?id=1100000000816735030

This C98 does not take 2^21 ecm curves using Yafu.

Giving the mentioned C165 a try right now.

storflyt32 · 2016-01-21, 23:38

http://factordb.com/index.php?id=1100000000816947847

http://factordb.com/index.php?id=1100000000816969374

This number has a P151 when "divided" from RSA-1024 and next factorized a little.

But here I only have the C149, not the individual factors for this number.

Any suggestions welcome.

Edit: Thanks for the previous one!

storflyt32 · 2016-01-22, 04:33

More importantly, we should not forget about the difference between factor finding and large prime numbers.

For such a reason, 2^52342403 - 1 is most likely not a prime number, while 2^5554984213877167-1 or 2^2814314134663434139939-1 well could be so.

Is it harder or easier to tell for sure that possibly either one of these numbers, or perhaps 920766^524288 + 1 for the Genefer prime search is prime by only looking at the syntax for such a number?

Where is the difference here? Could you please tell me the answer.

ET_ · 2016-01-24, 15:26

Quote:

Originally Posted by storflyt32

More importantly, we should not forget about the difference between factor finding and large prime numbers.

For such a reason, 2^52342403 - 1 is most likely not a prime number, while 2^5554984213877167-1 or 2^2814314134663434139939-1 well could be so.

Is it harder or easier to tell for sure that possibly either one of these numbers, or perhaps 920766^524288 + 1 for the Genefer prime search is prime by only looking at the syntax for such a number?

Where is the difference here? Could you please tell me the answer.

M5554984213877167 has a factor: 6488221561808531057 - Program: L5.0x
M2814314134663434139939 has a factor: 5097691021937803448773668017 - Program: L5.0x

Luigi

storflyt32 · 2016-01-25, 10:58

Did I really mention that above?

Anyway, thanks!

I am quite impressed.

Perhaps another question for you at the same time.

In some cases, prime numbers end up being divisors, for example Fermat divisors.

Assumedly such a thing can not be said about regular factors, because in most instances, the factors from one factorization do no divide from another composite number.

This makes factoring numbers like RSA-1024 and RSA-2048 particularly difficult.

Therefore, is there a special way of being able to come across such divisors and how is it then being done?

Thank you for any answers.

ET_ · 2016-01-25, 13:15

Quote:

Originally Posted by storflyt32

Therefore, is there a special way of being able to come across such divisors and how is it then being done?

Short answer: No.

Long answer: Factors of RSA numbers are carefully chosen among billions of possible pairs, to have no response against known attacks (factorization, dictionaries, bruteforce, ECM and even statistical ones).

The only known attack to get an RSA factored is the NFS (Number Field Sieve, look for it on Google), but even for a RSA896 the resources needed to complete the factorization in time, processors and memory requirements are above the single user possibility.

Take it for granted, as you re talking to a participant of the task force who factored RSA768...

2016-01-20, 13:53	#103
LaurV Romulan Interpreter Jun 2011 Thailand 7·1,373 Posts	Don't click reply to this bot's messages. Don't reply to him and don't post anymore in this thread. This thread is specially for him to talk alone. Otherwise he has notification set so it will get notified when someone reply, and will continue to troll the forum forever. Last fiddled with by ewmayer on 2016-01-21 at 02:09 Reason: GCD = "greatest computational doofus"?

2016-01-21, 03:50	#104
storflyt32 Feb 2013 2×229 Posts	http://factordb.com/index.php?id=1100000000816954288 http://factordb.com/index.php?id=1100000000816944358 http://factordb.com/index.php?id=1100000000816968957 Here is an example when it comes to the use of GCD. The third link is the dividing difference between the two first results. Edit: Perhaps a slight misunderstanding here. With my computer, I am not able to only factorize (or at least trying) one single number, but possibly be looking at one or more number, or sets of numbers against another number, or set of numbers. Possibly this may be the reason for the slight confusion here. You probably will not be able to factorize the C165 from what you already have, even when using GCD. Last fiddled with by storflyt32 on 2016-01-21 at 03:59

2016-01-21, 17:18	#105
storflyt32 Feb 2013 2·229 Posts	http://factordb.com/index.php?id=1100000000816735030 This C98 does not take 2^21 ecm curves using Yafu. Giving the mentioned C165 a try right now. Last fiddled with by storflyt32 on 2016-01-21 at 17:20

2016-01-21, 23:38	#106
storflyt32 Feb 2013 2·229 Posts	http://factordb.com/index.php?id=1100000000816947847 http://factordb.com/index.php?id=1100000000816969374 This number has a P151 when "divided" from RSA-1024 and next factorized a little. But here I only have the C149, not the individual factors for this number. Any suggestions welcome. Edit: Thanks for the previous one! Last fiddled with by storflyt32 on 2016-01-21 at 23:46

2016-01-22, 04:33	#107
storflyt32 Feb 2013 2·229 Posts	More importantly, we should not forget about the difference between factor finding and large prime numbers. For such a reason, 2^52342403 - 1 is most likely not a prime number, while 2^5554984213877167-1 or 2^2814314134663434139939-1 well could be so. Is it harder or easier to tell for sure that possibly either one of these numbers, or perhaps 920766^524288 + 1 for the Genefer prime search is prime by only looking at the syntax for such a number? Where is the difference here? Could you please tell me the answer. Last fiddled with by storflyt32 on 2016-01-22 at 04:36

2016-01-20, 04:17	#100
storflyt32 Feb 2013 458₁₀ Posts	Thanks for the suggestion, wblipp. But if I am not wrong, GCD will not be able to return the correct answer when one of the numbers are composite. Therefore I am not getting this working right now. Anyway, congratulations to you for the new Mersenne prime number. This is a great, or really magnificent find! You possibly already know that I happen not to be doing the same thing and you certainly already know why. If you do not know, I happened to get my knowledge about numbers by entering the wrong door, namely by means of +1 rather than -1. Is it possible to compare the total number of factors, or possibly prime numbers when looking at Mersenne numbers and factors versus Fermat factors? If being slightly terse in my language, there is no such thing as a Fermat prime, only Fermat factors and prime numbers which rather are being designated Genefer primes. In fact, a given number which could possibly be regarded as being a Fermat number still may be composite, because there remains at least one factor or perhaps more in order to have such a number fully factorized. At least one such number lies on my disc. It is a P245 and if added to the Factor Database makes the number it is one of the factors of fully factored. Other similar numbers lies on a disc on my shelf which is not bootable. It should be easy to understand that I am not readily able to factorize 100 down to 11. In the same way, neither 5 * 17 or 2 * 7 * 7 are not able to return 97. Also you certainly know that it could take quite a long time when the number is being large. There you have most of the problem in a nutshell. Compare with this number, for example, namely 7810^128 + 1 http://factordb.com/index.php?id=1100000000622746569 http://factordb.com/index.php?id=1100000000487350801 Because you are doing what you are supposed to be doing, you will not be able to give me any advice here. The C499 does not divide with the P215, by the way. For every answer or result being found, there remains yet another question to be solved.

2016-01-25, 10:58	#109
storflyt32 Feb 2013 458₁₀ Posts	Did I really mention that above? Anyway, thanks! I am quite impressed. Perhaps another question for you at the same time. In some cases, prime numbers end up being divisors, for example Fermat divisors. Assumedly such a thing can not be said about regular factors, because in most instances, the factors from one factorization do no divide from another composite number. This makes factoring numbers like RSA-1024 and RSA-2048 particularly difficult. Therefore, is there a special way of being able to come across such divisors and how is it then being done? Thank you for any answers. Last fiddled with by storflyt32 on 2016-01-25 at 11:05

Similar Threads
Thread	Thread Starter	Forum	Replies	Last Post
Can Pollard Rho cycles be used to find a factor?	wwf	Factoring	26	2013-09-30 04:24
PFGW can't find a small factor.	Arkadiusz	Software	7	2013-02-18 12:43
Chance to find an n-digit factor with ECM	RedGolpe	Factoring	4	2007-03-23 15:24
How much ECM does it take to find a given factor?	geoff	Factoring	5	2004-09-29 20:14
Where I find the best program to it factor keys? I use AMD.	chrow	Factoring	5	2004-02-19 10:15