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

10^444031*9-1 has a known factor 66666323.

Apparently there is a factor 114851129 of (10^444031*9-1)/66666323 as well.

It took quite a bit of time finding this small factor using Yafu's ECM command and for now I did not redirect the output to any file.

Therefore the whole process including the comparison of the numbers became more or less manual between three different DOS window boxes.

It takes only a few seconds to find by this (very slow) script:
[CODE]> gp -q
? p=66666321;
? while(1,p=nextprime(p+1);if(Mod(10,p)^444031*9==1, print(p)))
66666323
114851129[/CODE]

A question for you.

This number:

[URL]http://factordb.com/index.php?query=2%5E4096%2B1[/URL]

The composite number there (a C1133) has not been factored. I know that there have been made several attempts, but for now without success.

Another number more indirectly related to this number is being found here.

[URL]http://factordb.com/index.php?query=376322477048617706282462388956027634343218845103390837212250702240959281150975236858250674636956552977575644992330996492338135918917204224925730238170019337820662498693330214493679906249430900443624368413333595681442733617839085943481006048777973773591406068191894247135076070607701671255689393354833931428904840400137034536160570869727614264736511398659942277301367066020633087558665671166875762563942035532792180363929088374279589503341188047214073086726851135261749578902508394601821973454790627006430017331868404601460469312723942289592524483574675347884177907988641059081276472500778218279942489601992074842988131294457842242038301712355434936375127073908356537956356729529445349120612641176599142068049970365809774454799542388248241553661260847138183261484650763885768211561752754874815731734124473715998503717723148675023907224588066094282547359309526247271656601476531496818804530635931377069937447283246131305098070657511838862477777176956021954715464471389371275116614094336106603451173330189453927144813866143757504892797659528403039717804532780633926183197591614987388529999585227478353262018919671[/URL]

Perhaps I should rather tell you that I do have a factor for this number lying around. It is a somewhat larger factor, a P34, to be more precise.

I will need to carry out the factorization once again, because I have lost it. For now I only do have the mentioned factor available.

It is not related.

It is a cofactor of
(2^4096+1)/25860116183332395113497853167940236083358054\ 650286886725246241569916604094012679963198712829716480001[COLOR="Red"]-2[/COLOR]
not of 2^4096+1

ans = 10906594903029791068395400811884464627409515459009973450004302442452725255227

P35 = 62611614700115894971255725399191227

P42 = 174194435892891975029270196982744708432001

Very long factor(s), good catch. Do you plan to report them to mersenne.org ?

Thanks!

Anyway, I notice a problem with the Yafu factoring software.

I am having a 64-bit computer, so I am using both the 32-bits and 64-bits versions of this software.

Apparently the 32-bit version is returning the wrong co-factor number in the result. This has now become a very annoying feature and needs to be fixed as soon as possible.

Thanks again!

If you are reporting a bug, please list the YAFU version number, and the composite & result so someone else can try to reproduce it.

[QUOTE=storflyt32;385008]ans = 10906594903029791068395400811884464627409515459009973450004302442452725255227

P35 = 62611614700115894971255725399191227

P42 = 174194435892891975029270196982744708432001[/QUOTE]
What is this number, anyway?

ans = 5687625641025641025641025641025641025641025641025641025641025641025641025641

P33 = 213843479182611070647190753814939

P44 = 26597143213184949293331777384754973697286219

I *guess* he is factoring the "smallest composite without known factors" from the factordb, those are also 76 digits.

On my laptop those C76s take at most 5 minutes to factor using YAFU and are not worth reporting.

Thanks for reminding me about that.

Working on a C83 right now.

I posted here because there was an upload problem of the results.

Thanks for giving me a hand!

But the important thing is really the assumption that all numbers in fact are linked to each other, regardless of size or composition.

Factoring numbers more or less in sequence may partly solve the given problem, but also we know that there are some unanswered questions.

I earlier mentioned the composite factor of 2^4096+1. Am I perhaps wrong, but is not such a problem being attempted solved by means of an "approximation"?

Being able to factorize a number makes the remaining part of the problem a little bit smaller, of course. In the end you may go through all the numbers that you have and may be able to "pick" the missing number(s) from the list that you are having.

Most likely you may be able to solve the problem this hard way, but it may take a long time to do just that.

[QUOTE=storflyt32;385237]Thanks for reminding me about that.

Working on a C83 right now.

I posted here because there was an upload problem of the results.

Thanks for giving me a hand!

But the important thing is really the assumption that all numbers in fact are linked to each other, regardless of size or composition.

Factoring numbers more or less in sequence may partly solve the given problem, but also we know that there are some unanswered questions.

I earlier mentioned the composite factor of 2^4096+1. Am I perhaps wrong, but is not such a problem being attempted solved by means of an "approximation"?

Being able to factorize a number makes the remaining part of the problem a little bit smaller, of course. In the end you may go through all the numbers that you have and may be able to "pick" the missing number(s) from the list that you are having.

Most likely you may be able to solve the problem this hard way, but it may take a long time to do just that.[/QUOTE]

Word Salad. Meaningless gibberish.

Exactly.

[URL]http://factordb.com/index.php?id=1100000000716601856[/URL]

One more problem solved. One less to go.

But are you still getting the whole picture?

Yes, I do know that this web-page are all about Mersenne numbers.

I do a little bit a prime number cracking. My account data for this is found here:

[URL]http://www.primegrid.com/show_user.php?userid=170706[/URL]


We happen to know about the largest prime number being a Mersenne number, because of an assumption that those numbers having a -1 is a little bit easier to "crack" than a similar +1 number, like a Proth number or a Genefer number for that matter.

So what is the "probability" of finding a prime number when comparing a Mersenne number against a Genefer number? Am I standing a better chance of finding a prime by means of using the Prime95 client.

I shall be looking around and see if a can find this application once more.

Unfortunately I have not had the opportunity at using this client for a little while because of both hard disc problems as well as a couple of other things as well.

[URL]http://factordb.com/index.php?query=%282%5E67303*101%2B1%29%2F7[/URL]

The remaining number is a composite, C20250, but apparently not working here. Tried using both Yafu-win32 as well as Yafu-x64.

Just added a PRP1080 to our current knowledge.

The web-link is for now a little long when it comes to syntax, so please let me know if you are interested.

[QUOTE=storflyt32;385244][URL]http://factordb.com/index.php?query=%282%5E67303*101%2B1%29%2F7[/URL]

The remaining number is a composite, C20250, but apparently not working here. Tried using both Yafu-win32 as well as Yafu-x64.[/QUOTE]

You should try reading the documentation that comes with yafu, ecm, and the other factorization software (msieve in particular has a good readme). Your observation that YAFU does not work on a 20k digit number is a little like remarking that you are disappointed that a hand axe failed to split the earth's crust. msieve readme will explain what size problems can be factored with each factorization method, hopefully preventing you from trying to split the Earth next time.

You say you like to crack prime numbers- that's usually quite difficult, per the definition of "prime".

The numbers that you are describing as new knowledge are just like water sloshing back and forth at an ocean beach. Now look at the vastness of the whole ocean. Think for a moment. And stop posting things that are being posted by thousands of other people silently to factordb.com at a speed of ten per second. Does each of them deserve a posting? Ten postings to mersenneforum per second with just bare numbers?
[QUOTE]ans = 5687625641025641025641025641025641025641025641025641025641025641025641025641

P33 = 213843479182611070647190753814939

P44 = 26597143213184949293331777384754973697286219[/QUOTE]
That's what factordb.com is for, not the mersenneforum!

Post a few more and you will get a day ban for posting, then a week, then a month. this already happened to the user "[COLOR="DarkOrchid"]cmd[/COLOR]", so you will be in a good company.

Which factors are there for 2^48853-1, if I may ask?

Also, why not give a try on 2^(2^20)+1 ( or 2^(2^20)-1 ) for that matter?

Definitely you should be able to find a decent prime in such a number.

Have you tried checking [url]http://factordb.com/index.php?query=2%5E48853-1[/url]? I hear it's a good source of information.

Apparently the P(RP)1764 in that number was pulled out again :(

What was pulled out again? The prime cofactor of the algebraic factor (2^6979-1)/(2^997-1), a.k.a. Phi[SUB]7[/SUB](2^997)? It's there.

Still getting a C41715 here both from yafu-x64's "factor" command and also by running the ecm command also with yafu-x64.

This time having the output to the screen (or monitor) instead of a file.

Took a bit of time to get the

=============================================
ecm: 0/1 curves on C41715, B1=11K, B2=gmp-ecm default

visible.

[QUOTE=storflyt32;385591]Still getting a C41715 here both from yafu-x64's "factor" command and also by running the ecm command also with yafu-x64.

This time having the output to the screen (or monitor) instead of a file.

Took a bit of time to get the

=============================================
ecm: 0/1 curves on C41715, B1=11K, B2=gmp-ecm default

visible.[/QUOTE]

I assume you are still going on about [URL="http://www.mersenneforum.org/showthread.php?t=19772"]this[/URL]. Just because you can print it does not make it so.

I am sorry that yafu does not work on every conceivable input, but the fact remains that it was not designed to work on numbers like this. Why would you insist that yafu is right when every other piece of software that *was* designed for numbers like this disagree with it?

Do not know where to post this.

[url]http://factordb.com/index.php?id=1100000000785525326[/url]

Lying at the bottom of my checkfacts.txt file, the number fits into the factorize line in the Factor Database.

Just clicking the Factorize button, it first became "U" for unknown.

Clicking the button again and I was told it was a PRP3759.

This time it apparently was not because of me.

Whose responsibility is to update what and where and if a given number turns out to be a quite large one,
who should be credited with the find or discovery?

[QUOTE=storflyt32;404695]Do not know where to post this.

[URL]http://factordb.com/index.php?id=1100000000785525326[/URL]

Lying at the bottom of my checkfacts.txt file, the number fits into the factorize line in the Factor Database.

Just clicking the Factorize button, it first became "U" for unknown.

Clicking the button again and I was told it was a PRP3759.

This time it apparently was not because of me.

Whose responsibility is to update what and where and if a given number turns out to be a quite large one,
who should be credited with the find or discovery?[/QUOTE]
The factordb server probably ran a PRP check.
On the status page, one core of the 2600k is dedicated to do this:
"Checking the smallest number with status unknown <20000 digits"

:whistle:

[url]http://factordb.com/index.php?id=1100000000792308300[/url]

The remaining C103 is a very difficult one.

Running it using ecm only could possibly work, but would probably take a very long time, depending on the number of curves which are being selected.

Most likely the 9704 curves being used by the Yafu software is not enough for this number.

Therefore a larger number of curves are needed, increasing the number it takes to complete.

You don't have an hour to factor this yourself?

[QUOTE=jasonp;405927]You don't have an hour to factor this yourself?[/QUOTE]Actually, a little more than an hour, but then I couldn't run my full 6 cores becuase of the ambient temp....

I notice the factorization of the remaining C103.

Thank you very much for doing that.

Appreciated.

Here is another interesting one. I have recently stumbled onto this C81 ([URL="http://factordb.com/index.php?id=1100000000792511003"]link[/URL]). This will be a difficult one to crack. In fact, it will likely take longer than the age of the universe to factor. I have already started trial factoring with my pocket calculator, and will let you all know of any results.

[QUOTE=Jayder;405983]Here is another interesting one. I have recently stumbled onto this C81 ([URL="http://factordb.com/index.php?id=1100000000792511003"]link[/URL]). This will be a difficult one to crack. In fact, it will likely take longer than the age of the universe to factor.[/QUOTE]

I hope you meant it ironically?

Same person finds different factor via ECM and PM1 on the same day
 

[CODE]Mn Status Details
131009 Factored 1937759097343
15368075063617012721
469572650565399789119183
251874321670721973902750994646081
History
Date User Type Result
2015-07-17 BloodIce F-ECM Factor: 469572650565399789119183 / (ECM curve 99, B1=250000, B2=25000000)
2015-07-17 BloodIce F-PM1 Factor: 251874321670721973902750994646081 / (P-1, B1=50000000)
2009-03-05 ANONYMOUS F-ECM Factor: 15368075063617012721[/CODE]

[QUOTE=VictordeHolland;406005]I hope you meant it ironically?[/QUOTE]
I hope so.

Hi, Jayder.

Try multiplying Mersenne 48 with the factor 3, next try factorizing the number you get.

It should not be that difficult.

If I happen to multiply a known RSA factor with a Fermat factor, I might end up at a number like this,

19036657588412969111505965532704495313206606970654378333477575250997660572
96146492268504477755829049148371391847449774943227537240957345732440163922533773
3449295565780737

It is a C170, by the way.

Try factorizing this number.

Based on the information given, it should not be an impossible thing to do.

Edit:

I only read page 3 here before posting. The last page for some reason slipped my fingers.

[url]http://factordb.com/index.php?id=1100000000792565896[/url]

If you are having the time.

[QUOTE=storflyt32;406020]Hi, Jayder.
If I happen to multiply a known RSA factor with a Fermat factor, I might end up at a number like this,

19036657588412969111505965532704495313206606970654378333477575250997660572
96146492268504477755829049148371391847449774943227537240957345732440163922533773
3449295565780737

It is a C170, by the way.

Try factorizing this number.

Based on the information given, it should not be an impossible thing to do.

[/QUOTE]

Just trying Fermat numbers from 2^2+1 upwards in factordb I soon found 2^4096+1 has a common factor with it. I could have written a program to do it, but that would have taken longer than trying them by hand.

Chris

Thanks!

Also while noticing the other one as well, I took the time of doing the same with the other P116 of RSA-232.

But perhaps this was not a result of factorization skills or ability, but rather something else instead.

Found a factor for [URL="http://www.mersenne.ca/exponent/12408313"]exponent 12408313[/URL] through P-1. Two factors actually. The pc used E=12 for the factoring and came up with a B2 limit for regular P-1 just 10% under a billion. Nice found.

(4331*2^1255628+1) has factors 3, 3 and 7 (63)

The remaining part is composite.


pfgw64 -q"((4331*2^1255628+1)/63)"
PFGW Version 3.7.7.64BIT.20130722.Win_Dev [GWNUM 27.11]

((4331*2^1255628+1)/63) is composite: RES64: [05A11D83AA626AEE] (1756.0910s+0.0013s)

[url]http://factordb.com/index.php?id=1100000000803014320[/url]

The initial C169 there.

Added the P18 right now. The rest or remaining is still in the blue.

Try "dividing" the C1133 of (2^4096+1) on this C169 and see what you get.

I could add this factor as well.

[url]http://factordb.com/index.php?id=1100000000803014664[/url]

My best one in a little while.

C156 = 1046549594684669247529542854996104560606610105651308122647323036788396252
83702968161057585901197429244373750447622645448631676673651879291916651670550446
647

[url]http://factordb.com/index.php?id=1100000000226834094[/url]

"Divide" this number from RSA-1024 above and and next factor it and you get a P152 back in return.

[url]http://factordb.com/index.php?id=1100000000803112399[/url]

Done already for orders sake.

Found a quite large factor here only two minutes ago

A PRP882.

[url]http://factordb.com/index.php?id=1100000000803360398[/url]

P31 = 1001257397059038591699252193963

Manually at least. Crashes out when using Yafu. Ecm gives nothing here as yet.

[url]http://factordb.com/index.php?id=1100000000803360552[/url]

Added the PRP882,

[url]http://factordb.com/index.php?id=1100000000803360400[/url]

Better say thanks.

[QUOTE=storflyt32;410738]Better say thanks.[/QUOTE]For what?

Because not being a part of the whole picture.

Read - stupid people.

[QUOTE=storflyt32;410756]Because not being a part of the whole picture.

Read - stupid people.[/QUOTE]

You are a few kegs short of a six-pack.

Isn't storflyt32 a troll bot? That was my understanding from another thread -- it just posts semi-coherent gibberish that people waste time replying to.

[QUOTE=danaj;410767]Isn't storflyt32 a troll bot? That was my understanding from another thread -- it just posts semi-coherent gibberish that people waste time replying to.[/QUOTE]

Then one must ask: Why isn't it banned?

[QUOTE=R.D. Silverman;410768]Then one must ask: Why isn't it banned?[/QUOTE]

Various discussion for and against [URL="http://www.mersenneforum.org/showthread.php?t=19772&page=10"]on this thread[/URL].

Personally I find it quite annoying, as a useful productive thread with actual content sometimes gets random interjections that either just clutter or make people go off on a tangent replying to them. This sometimes happens with old threads, which he/she/it picks to revive. From what I can tell, in the hopes of wasting everyone's time. I don't know any other way to describe the behavior other than trolling.

[url]http://factordb.com/index.php?id=1100000000803426215[/url]

This by means of factorization.

I did not have the factors here, but noticed earlier that something like this could become the result.

Therefore being not totally surprised here.

[QUOTE=danaj;410770]This sometimes happens with old threads, which he/she/it picks to revive. From what I can tell, in the hopes of wasting everyone's time. I don't know any other way to describe the behavior other than trolling.[/QUOTE]
Sounds like a fair assessment. By multiple people.

Continuing with a month ban for spam. (1, 3, 7 days have been imposed in the past.)

Apparently back.

Having the keypad on a separate table below the main table made it a comma rather than a punctuation mark in an earlier post. My apologies.

Please have a look here.

[url]http://factordb.com/index.php?id=1100000000804918686[/url]

The C129 at the end there.

[url]http://factordb.com/index.php?id=1100000000804918607[/url]

Multiplying the C129 with the C148, next taking the square root of this number using the built-in function in Yafu, I get this
factorization, which apparently is a bit more simpler.

[url]http://factordb.com/index.php?id=1100000000804928303[/url]

The C148 apparently is a very difficult number to factorize. The C129 may be somewhat easier.

Are such factorization attempts still possible or available by means of using distributed computing?

Yes, I happen to know that NFS@home is supposed to be doing a couple of such things, but then you need to know in advance which numbers are supposed to be hard to factorize and worth the possible effort.

What is this thread still doing on Factoring?
...moving now.

[QUOTE=Batalov;414362]What is this thread still doing on Factoring?
...moving now.[/QUOTE]
Probably because of the habit of some mods to rename threads, this was confused with the regular "found a factor? call the police!" or whatever is called now the other, more serious one, and no mod checked what is inside. I also saw the thread title and didn't go inside, assuming is the other one, with title change. Which new title I actually liked, but didn't waste to time to click it. I clicked it now only because I saw your post being last and I never lose the chance to learn something new from your posts. Now, disappointment :razz:

OTOH, we love bots. They never get angry, never get emotional, they always follow their logic, they always have funny problems to solve, they always are compassional, and always apologize making an elephant from a mosquito, like the dot replaced by a comma... and they never get angry (did I say that?).

It was a quiet month...

:ban:

I also vote in favor for another very lenghty ban. Again posts factors of random small composites, where he/she was previously banned for.

If I may.

You are right that this section is not about factoring.

My apologies for that.

But here is an interesting point.

While the Factor Database is having a huge collection of numbers being composite, consisting of mainly smaller factors, such numbers are assuming to be excluding those numbers which eventually end up remaining and may show up to be true.

In many cases such number becomes composite only, because the individual factors making up such numbers become too hard to factorize.

Example of this are semiprime numbers, of which several are known, assumedly based on trial division and not necessarily factoring.

More factors for the Mersenne numbers which are known to be composite are being found and a similar project is also being carried out for Proth or Genefer numbers as well, which also may be having the name Seventeen or Bust for the first one.

For these numbers we probably do not know any large semiprimes, but one may suspect that the RSA numbers could be a deviation or variant of such numbers.

Right now I do not find a numerical example which may show the format of a RSA-4096 based number. Such numbers are only known to be composite when starting with RSA-1024, but they should be having only two factors.

Finding a prime number larger than Mersenne 48 probably will be a difficult thing to do and such a thing will likely not be accomplished in the near future.

[QUOTE=storflyt32;414458]If I may.[/QUOTE]

You may.

[QUOTE=storflyt32;414458]Finding a prime number larger than Mersenne 48 probably will be a difficult thing to do and such a thing will likely not be accomplished in the near future.[/QUOTE]

Probably true.

[url]http://factordb.com/index.php?id=1100000000804985231[/url]

[url]http://factordb.com/index.php?id=1100000000804869672[/url]


I notice the factorization of the C100 there, which for the moment became slightly too large for me to be dealing with.

Thank you to the one who carried out that factorization.

But when "dividing" this number from RSA-1024 and next factorizing this number, although possibly getting some smaller factors at first, one might assume that the remaining number could be slightly easier to factorize.

But it is not. In the same way I am getting a number which is larger and probably even more difficult to factorize.

What I am able to see is that a number like RSA-1024 is in fact a based on a three-way or more factorization principle.

Rather than having one set of factors helping out determining the remaining part of the number, at least three separate
factorizations are needed and each of these ones could take a considerable amount of time.

Adding to this the total number of different combinations of numbers which are difficult to factorize as well and it becomes
easy to understand the total difficulty when it comes to the whole problem.

We are lead to believe that the factors of RSA-1024 are being known by RSA labs by means of multiplying two individually chosen factors with each other giving the composite, publicly known number.

Is this true? Can it be proven that the individual factors for this number as well as a couple of other ones are being known?

These numbers are supposed to be impossible to factorize. Still, being able to determine whether or not a number having some 154 or 155 digits is prime or not is possible to do in a couple of seconds.

Theoretically one could attempt finding these numbers in a pure sequential way, starting with an odd 154 digit number not ending with 5 and ending with a 155 digit number of the same, checking each one for possible primality.

However, doing such a thing this way is not the best option at least when it comes to variation and possible differences between the numbers. Therefore it should not be a good option having any such listing of numbers being in consecutive or sequential order.

Apparently nothing much new here.

Is a composite number supposed to be having certain or particular factors based on a specific or particular approach when it comes to a given problem?

This number, C48 = 483187363867474790571693776572872797307789738881, is a composite number.

It should be easy to factorize.

Most or every factor of this number should be regarded as being a Fermat factor, or at least belong to a related or similar series of factors.

You are not supposed to be dividing such a composite number with a factor being a part of a Mersenne number known to be composite, because such a number would not be a factor of such a number.

So, where the number having the largest known Fermat factor becomes known, you may start think that perhaps a number being a factor of a Mersenne number should happen to be such a Fermat factor.

As mentioned, this happens not to be true.

You only may be able to know that a factor, or a set of factors, may belong to a composite number by means of the factors you are able to come up with by means of the factorization of such a number.

Possibly someone may be having the thought or impression that maybe an unknown RSA number could be the factor of such a composite number, but for now such a thing is impossible to prove, both because such numbers may not necessarily be factorized when being smaller and therefore not be known to be factors of the even larger composite numbers.

Or perhaps "given or specific factors based on a particular approach" instead for better wording.

Too late to edit the previous post.

Should perhaps tell I had a somewhat difficult day.

There are a couple of problems in my home.

But I have been having a couple of private messages from science_man_88 regarding a couple of interesting things which are or happen to be known about factors and their respective syntax.

If a cake for some reason is very large, you are not always able to have all of it together with a cup of coffee.

At least you may need to divide it into two pieces at times.

The same may not be said when it comes to the factorization of certain numbers, like large composite numbers, semiprime numbers and RSA numbers.

In order to be able to factorize some numbers, you may need to find some number in between, in the hope that such a number may be easier to factorize.

If a number is being large, the number of different combinations becomes large as well.

Consider this example.

From a randomly selected lookup, I was able to find that 2^39183121 is having 8 known factors.

235098727, 626929937, 3761579617, 16927108273, 48822168767, 1507374664871, 15337840884241, 247223472595999

If I choose to multiply these factors with each other, I get the number

2618873532522135207992307037237914903436166716609918326901333144023400091020038941631617

If I next try dividing RSA-1024 with this factor, I get this result

[url]http://factordb.com/index.php?id=1100000000805326217[/url]

Only one example among many others.

Definitely this does not readily show up, but perhaps such a thing should be assumed if you happen to be doing these things.

This goes to show that the number of different combinations are huge. Some factorizations are better than others, but whether or not some of these should be regarded as being possible "brute force" attempts, they are still not able to return the correct solution.

I have possibly mentioned this earlier, but there could be a guess that the factors of RSA-1024 or RSA-2048 may not be known at all.

These numbers are in fact the result of factorizations of even larger numbers and this is where it ends for the moment.

These numbers are being used for privacy on the web, including possible certificates, as well as the http protocol and a way to encrypt data using this protocol...

As an illustration, consider a long bar mounted with its central point on a fixed point or mount towards the ground being used in a kindergarten.

There may be several children having different sizes or weight sitting on each side of the central point and the bar is going up and down on each side as the long bar goes up and down on each side. If a large child is sitting in the middle on one side, the bar will only go slightly down on the other side if a smal child seats down close to the central point. Slightly more if the small child rather choose to sit at the end of the bar on his side.

The same goes for the factorization of numbers as well. A small number may be "divided" from a large one returning a possible large factor, but not necessarily the correct factorization of the whole number. A larger number being used for the division may return a smaller factor as a result, but still not necessarily the correct factorization in the same way.

Therefore it may be a reason to ask what the possible "optimal" set of factor cominations should be assumed to be if a given number may not be factorized, even when using "brute force". Again, larger factors should be regarded as being better than small one, but still you may not be able to factorize a given number in this way.

I think you should read a book about basic number theory. I suggest the book [i]A First Course in Number Theory[/i] by Hugh M. Edgar. You can get it through Amazon.com for $2,629.01 + $3.99 shipping.

Became a little long.

Thanks for the tip, by the way. Did not notice after posting.

But found another good example.


[url]http://factordb.com/index.php?id=1100000000805440883[/url]

[url]http://factordb.com/index.php?id=1100000000805440839[/url]


The P40 and P50 in the first link is a better one.

Not me this time. Thanks to the one who did that job.

But the second link apparently is a quite difficult one.

Here I do not have the bit length or the similar, but possibly this number could be as difficult as a RSA-512.

The evident fact is that even though the factors may be found for this number, you already know that they will not be factors of RSA-1024.

If 35 for some reason is the big composite number you would like to factorize, you already know that some number in between which is composite, like 12 or 18, may not be having factors of 35.

Even prime factors, like 3, 11, 13, 17, or 19 will not be the same when it comes to being so.

Easy to say when the numbers are small, but when they grow in size, the numbers in between become many more.

Therefore, rather than asking the question about the possible factors of a given number, like RSA-1024, it may better be asked a couple of questions about the way specific factors are being determined in a similar way.

RSA-512 apparently became factored by means of the usual factorization.

RSA-768 is supposed to have been factored in the same way.

Therefore, if a number is not supposed to be readily factorized, in which way are you supposed to be able to determine the exact or precise factors for a number where such a factorization is supposed to be possible?

Right now there apparently is no clear answer to this question.

[QUOTE][FONT=inherit]Have you heard of a [URL="https://en.wikipedia.org/wiki/The_Good_Soldier_%C5%A0vejk"]Good Soldier Schweik[/URL]? It is a fictional character created by a Czech writer Jaroslav Hasek in 1914 but still popular all around the world.[/FONT] [CENTER]
[/CENTER]
[LEFT] [FONT=inherit]At some point in the book Schweik demonstrates such enthusiasm in serving the Emperor that his sanity is questioned and he appears before the medical board. He is asked by the certified psychologists:[/FONT][/LEFT]
[I][FONT=inherit]"Is radium heavier than lead?"[/FONT][/I]
[FONT=inherit][I][B]"Please sir, I haven't weighed it,"[/B][/I] answered [/FONT]Schweik[FONT=inherit] with his sweet smile.[/FONT]
[I][FONT=inherit]"Do you believe in the end of the world?"[/FONT][/I]
[FONT=inherit][I][B]"I'd have to see that end first,"[/B][/I] [/FONT]Schweik[FONT=inherit] answered nonchalantly. [I][B]"But certainly I shan't see it tomorrow."[/B][/I][/FONT]
[I][FONT=inherit]"Would you know how to calculate the diameter of the globe?"[/FONT][/I]
[FONT=inherit][I][B]"No, I'm afraid I wouldn't,"[/B][/I] answered [/FONT]Schweik[FONT=inherit][FONT=inherit],[/FONT] [B][I]"but I'd like to ask you a riddle myself, gentlemen. Take a three-storied house, with eight windows on each floor. On the roof there are two dormer windows and two chimneys. On every floor there are two tenants. And now, tell me, gentlemen, in what year the valet's grandmother died?"[/I][/B][/FONT]
[/QUOTE]...And now, tell us, storflyt32, in what year the valet's grandmother died?

Most of your circular arguments go around something that seems to be visible only to you through your magic glasses.

"This is a factor of this, and that is a factor of that, and I don't even know the factors of that third one... so now we finally know that they [B]will not be factors[/B] of RSA-1024." WTF? Why? "If 35 for some reason is the big composite number you would like to factorize, you already know ... bla-bla-bla... " -- what do we already know then? That 35 = 5 * 7 and now we finally know that 5 or 7 will never divide anything else in the world?? They've been "spent"? They've been so tired from dividing 35 that they will never divide anything else? Or what is it?

I think storflyt32 is basically saying that like fermat factors and mersenne factors ( which apparently aren't supposed to mingle something I didn't know) the factors of RSA number may not mix and so we can eliminate the factors of one form factors of the other ?

[url]http://factordb.com/index.php?id=1100000000805495792[/url]

Here you may find an example where different types of numbers are relating to each other.

[QUOTE=storflyt32;415463]... may not be having ...[/QUOTE]From India? I've encountered that English formation a lot in India. I be having memories of being in India now.

[url]http://factordb.com/index.php?id=1100000000805512949[/url]

[url]http://factordb.com/index.php?id=1100000000805512928[/url]


The initial C131 in the first link.

Should I perhaps factorize this number before reporting the factors?

Or perhaps I already did so.

Fair warning
 

[QUOTE=storflyt32;415529][URL]http://factordb.com/index.php?id=1100000000805512949[/URL]

[URL]http://factordb.com/index.php?id=1100000000805512928[/URL]


The initial C131 in the first link.

Should I perhaps factorize this number before reporting the factors?

Or perhaps I already did so.[/QUOTE]
[COLOR=Red][MOD HAT ON /] Fair warning:[/COLOR] Post another couple of useless factordb.com links and you will be banned for spamming.
[COLOR=Red][OFF /][/COLOR]

Psst, or hush.

Should perhaps not be telling, but here I just came across two factors which are having only
P1 = 2 and P1 = 7 in between before dividing RSA-2048.

Both ways, that is.

I will not be mentioning the factors here, but suffice to say that they are a P296 and a P320, respectively.

Multiplying the two factors and it becomes a C616 as a result,

Still have to multiply by 14 in order to catch up with the desired number.

At least when dividing, I get 14 back in return, which is 2 * 7.

This result ends up in my notes.

So perhaps a fair or honest question about something else, since I was lucky this time.

Right now the Mersenne primes are the largest known prime numbers.

Their syntax are ending with -1.

So, for some other numbers related to prime number finding, including the PrimeGrid 321 Search, The Riesel Problem and Woodall Prime Search, the same syntax is being common, although 321 also is dealing with +1 in its syntax.

Is it possible to make a correspondence or relationship between the sizes of the prime numbers that could be found for such projects when comparing just the different syntaxes for these numbers?

You may be able to find a megaprime by means of running either a 321 LLR or a Riesel LLR task, but these numbers may not be able to beat any Mersenne prime when it comes to its size.

Definitely all these projects are dealing with numbers that are being computed respective to their ranges.

A specific number for k, b or p, or the similar determines the exact size of the whole number, or possibly its composition.

The number for n is determining the total size of the whole number. Multiplying for example k with n and next adding or subtracting 1 could possibly determine whether or not such a number is prime.

Any answers are welcome.

[QUOTE=storflyt32;415616]Is it possible to make a correspondence or relationship between the sizes of the prime numbers that could be found for such projects when comparing just the different syntaxes for these numbers?
[/QUOTE]

I think the problem is that some algorithms don't even need to know of a factor ( mersenne numbers have the LL test to tell if they are composite for example only relying on the exponent for the number of iterations.) so syntax of the number itself is only needed to weed things out. if you look at the mersenne factor candidate form 2kp+1 you can form any odd number greater than or equal to 5 so in theory you could find any size prime by trial factoring a mersenne number without limits in theory. so other than the time it takes there's probably no ratio you'll find that stays still ( I may be wrong).

Anyone notice Carsten's big little find.
 

[url]http://www.mersenne.org/report_exponent/?exp_lo=14009&full=1[/url]

[QUOTE=petrw1;415629][URL]http://www.mersenne.org/report_exponent/?exp_lo=14009&full=1[/URL][/QUOTE]
Ha! now you got tricked to post here too! :razz:
Wrong thread.
See my post #59

[QUOTE=petrw1;415629][url]http://www.mersenne.org/report_exponent/?exp_lo=14009&full=1[/url][/QUOTE]

[QUOTE=LaurV;415665]Ha! now you got tricked to post here too! :razz:
Wrong thread.
See my post #59[/QUOTE]

Assuming that these posts are moved appropriately (curse you mods and your title changes :razz:), what was the sigma?

Here I was excited that this thread had gained some interesting content.. gossiping about factors that others found seems within the scope of this otherwise useless location.

Have a look here, please.


[url]http://factordb.com/index.php?id=1100000000805654118[/url]

[url]http://factordb.com/index.php?id=1100000000805654221[/url]


The C139 in the second link.

Here it apparently meets at an almost 90 degree angle.

The two factors were found separately, so no need giving this one a try.

I will update this one a little later.

[url]http://factordb.com/index.php?id=1100000000805963658[/url]

Really, I did have the P23 and P27 here and was working on the remaining two.

Apparently it became work done this time as well.

[QUOTE=Batalov;415556][COLOR=Red][MOD HAT ON /] Fair warning:[/COLOR] Post another couple of useless factordb.com links and you will be banned for spamming.
[COLOR=Red][OFF /][/COLOR][/QUOTE]
storflyt32: Don't say you haven't been warned. Go spam somewhere else for a month.

Congratulations with your lucky hit.

I am able to find this.

[url]http://factordb.com/index.php?id=1100000000812506211[/url]

If I choose to "divide this number (the C107) from RSA-1024, I apparently end up with a C203, which again has been factorized into a C186.

So if I choose the More information icon, I next am able to see that there could be added a P11 (P11 = 10275403429), as a product or factor, making up a number which is slightly larger.

[url]http://factordb.com/index.php?id=1100000000812506210[/url]

If I next "divide" RSA-1024 with this number and next start factorizing, you are able to get a little farther, but only with getting rather some smaller factors this time.

[url]http://factordb.com/index.php?id=1100000000812694618[/url]

Next "dividing" RSA-1024 with the FF117 (which could be assumed to be a C117) as well when being used in such a "dividing" fashion.

[url]http://factordb.com/index.php?id=1100000000812694637[/url]

This leaves me with the following question here. Which number of the C186 or the C163 is the most difficult one to factorize?

My guess is that the C186 is the more difficult number to factorize in this case.

Became a little too much to handle here. Really when saying I or me, it could in fact be you as well, or maybe vice versa.

Hope the meaning of it became clear.

Edit: Possibly getting it wrong here. The C186 is having a P31 factor.

oh no, he is back! happy new year... :smile:

Thank you very much!

[url]http://factordb.com/index.php?id=1100000000812713232[/url]

I was able to fully factorize this number a short while ago.

The P18 is an easy one to factor.

The remaining number was previously a C182, but this number became factored in only some 2917 seconds.

[url]http://factordb.com/index.php?id=1100000000812713241[/url]

Here is the mirror, or opposite number of this factor around RSA-1024.

Take the three largest factors in the first link and add (or multiply) the P18 in order to get the second link.

The C106 in the second link most likely is a quite difficult one to factorize.

Anyway, just for your information, I am able to see that RSA-2048 "divided" with 2^1279-1 has not been fully factored.

[url]http://factordb.com/index.php?id=1100000000812734033[/url]

Giving the C197 a try right now.

Right now I do not have an example ready, but came across a random example.

If for some reason I should be factoring a number other than RSA-1024 or RSA-2048 using Yafu, I could be able to find that a number may be having a P15, P20 and P23 as its factors.

Then, "dividing" the product of these three numbers from RSA-1024, I am able to get the following answer.

[url]http://factordb.com/index.php?id=1100000000815105869[/url]

[url]http://factordb.com/index.php?id=1100000000815106238[/url]

For now limiting the factorization of the second link to ecm(ans,30) for the C209.

Yes, I happen to know that four factors are better than three when it comes to this, but that is not about the question that I am asking.

It should be a fact that a number less than 309 digits for RSA-1024 may be having factors or numbers which are either composite or may be prime factors.

The total number of prime factors are the total amount of different numbers minus all numbers which are composite.

The total number of prime factors should be very large, but then why am I able to find only 7 factors (including 3 * 3), in the second link when limiting the factorization to ecm(ans,30) for the C209 ?

Is this because of the way factorization is supposed to be carried out by means of the software, or is it more because of the numbers in question themselves?

Any answers welcome.

[QUOTE=storflyt32;422650]
Is this because of the way factorization is supposed to be carried out by means of the software, or is it more because of the numbers in question themselves?

Any answers welcome.[/QUOTE]

No.

More specifically, you misuse the word divides, rending the rest of your post utterly useless gibberish. You have never found a factor of RSA1024, nor has any number you have ever mentioned divided it without remainder.
YAFU will not factor RSA1024. I invite you to try, and further to not post about it until it finishes.

Notice that I put the word "dividing" in apostrophes (" ").

Is it possible to "prove" in advance that the possible factors of the C209 will not be a factor or factors of RSA-1024?

Edit: Another example, slightly better.

[url]http://factordb.com/index.php?id=1100000000815112868[/url]

[url]http://factordb.com/index.php?id=1100000000815112893[/url]

For the first link I do have the factors for. Therefore it should not be wasted time on.

For the second link the C129 still remains to be factored.

Which one would be the better here? Is it possible to say or predict in advance?

Too late to edit the previous.

[url]http://factordb.com/index.php?id=1100000000815113546[/url]

[url]http://factordb.com/index.php?id=1100000000815113618[/url]

Would adding the factors in the second link be regarded as being "unfair"?

By, the way, a P114 and a P148 in the second link, found separately and possibly already known.

Should read "quotes" above, not "apostrophes".

:ban:

A question for you about the FDB right now.

Right now getting PRP rather than P for even smaller numbers being reported.

I have seen this before and since reporting of factors is being made "on the fly", no interaction is supposed to be carried out for at least the smaller numbers.

Why is this happening?

Is it a separate or specific mechanism being used to make a separation or distinction between those numbers which are supposed to be composite and those numbers which turn up being P or PRP and such a thing might possibly be turned off at certain times?

Any answers welcome.

The FDB has had a lot of new probable primes added to it and it's taking it a while to check if they are all really prime. Once that backlog has been cleared new primes will be proved quickly (if below 300 digits).

I don't know where they came from. It's annoying when it happens though.

Chris

[url]http://factordb.com/index.php?id=1100000000815557816[/url]