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

[Batalov]

Originally Posted by danaj

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.

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.)

[storflyt32]

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.

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

The C129 at the end there.

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

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.

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

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.

[Batalov]

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

[LaurV]

Originally Posted by Batalov

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

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

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...

[VictordeHolland]

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

[storflyt32]

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.

[chalsall]

Originally Posted by storflyt32

If I may.

You may.

Originally Posted by storflyt32

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.

Probably true.

[storflyt32]

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

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


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.

[storflyt32]

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.

[storflyt32]

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

Too late to edit the previous post.

[storflyt32]

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

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

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.