Except for the last page, the previous thread became a bit long. - Page 5

storflyt32 · 2017-07-01, 04:45

Making a new one here.

http://factordb.com/index.php?id=1100000000938270361

http://factordb.com/index.php?id=1100000000938278465

The C77, because it is still two factors, but next fully factored, I think was done on the server.

The C195 at the other end next is having a quite good factor as well, namely a P49, which could be added.

Still a C146 to go here though, so not yet finished here.

A couple of other factors as well in my list, which could be added first.

This when keying in n!-1 and n!+1 in the FDB, which is relating to that of Factorial numbers.

Here a little bit in the dark on the subject, but both Factorial numbers and Primorial numbers are part of the Project Staging Area at PrimeGrid.

The pocket calculator could be able to come up with 69! before unable to do any more, but next it becomes even at the end, before either subtracting or adding.

As usual not all the odd numbers being returned are prime either, but for each of these types we apparently are having record primes.

Perhaps a little more could be done with those numbers which are only composite or factors here, because finding anything larger could be a difficult thing.

Another thing, I happened to be something funny before signing off yesterday.

For that of Astronomy as a subject, we could be having the Arecibo message in our lists, or perhaps memory.

And here about a message being broadcast from Earth towards a globular cluster and not something that was picked up.

Making it a binary output or representation, it becomes some 23 lines and 79 columns of the whole message.

I chose to remove or omit the starting 0's and next used copy and paste in order to copy part of the output to Notepad.

Ending on a single line, with a couple of 1's in consecutive order at the end, the number, when being thought of as decimal such, is having factor P1 = 3 and the remaining number a
rep-digit factor or prime, some 300 - 400 digits or so.

Only to have it mentioned, because I am finishing off the rest of the beer right now, but could have it tomorrow.

So, while still having fun, of course keying it wrong and it becomes a P59 at the end.

http://factordb.com/index.php?id=1100000000938435249

http://factordb.com/index.php?id=1100000000938435263

P49 = 6384627520682549821072782803042294957487643979279

P59 = 24805184834556493674296971841383950146529962250161488466941

Both factors are known, but except for keying it wrong, also luck perhaps were striking back here as well.

http://factordb.com/index.php?id=1100000000938509033

Also mentioning a possible overcommitment at other places, but here not difficult at all, when next excluding the P14.

Total factoring time = 2938.1431 seconds

Having the coffee and cake shortly before 11:30 AM in the morning, because I sat the night over, I keyed in both n!-1 and n!+1 in the FDB for their respective outputs.

But if next doing the same related to the possible factorizations of RSA numbers, particularly those already known, my guess is that there is no similar syntax here.

http://factordb.com/index.php?id=1100000000937794539

Continuing here right now, because it could be an adjacent run, or factorization corresponding to this number.

Next needs checking, but as previously mentioned, got slightly overcommitted right now and experiencing a bit of difficulty.

http://factordb.com/index.php?id=1100000000938599206

http://factordb.com/index.php?id=1100000000938599225

Making it a new session here as well, here became a triple pair or set of factors which were not that difficult.

Total factoring time = 647.1420 seconds

The first one becomes a loose pair of P40 and P54 factors from my list and if you wish, you may give it a try.

Except for that, I could put these factors up here a bit later on.

Also that when looking at the results, the P38 and P50 pair of factors is definitely a quite nice pair from its appearance.

Also checking in with that funny looking C174, it now is at 600/7553 curves after finishing off both 2350 and 4480 curves first.

Either it becomes a restart first, but for now ETA is listed as 375.71 hours here and perhaps or probably will not succeed.

Now at 703/7553 curves and still running, ETA is now being given as 369.01 hours.

Also giving a try on the C145 in the middle, but here it could take some 6 more hours.

storflyt32 · 2017-07-07, 00:37

http://factordb.com/index.php?id=1100000000939236158

I could end up repeating myself because of having an Edit box open and next adding contents where it already may have been posted.

I will try to avoid it, but if so, I could edit it away later on if it happens.

But here an example of something neither easy or directly hard, but rather something in between, at least when it comes to my own computer.

I needed a break a short while ago and for now have not continued with the session, except for adding three more P100+ factors, without continuing from there.

And also it mostly blew right now, because it became a restart of the computer which I tried to abort, but next it turned or shut off without warning.

Back again after shuffling my equipment in the living room, because here it becomes a purchase of a second computer and also a quite powerful one.

So rather I gave the following a thought.

RSA-768 as you may know, is a 232 digit composite number having two P116 factors.

If I was unable to use the hard switch or button on this number, we probably could be having the discussion about cracking of numbers, or the similar, where

For now lacking the proper word or syntax which should be used here, but a similar discussion could be that of RSA numbers versus possible encryption, meaning cryptography.

Again, I am not into that subject, but still give a thought of the way a given number is supposed to be "cracked".

I prefer to make it that of numbers only, but still was able to come up with a name for such a number.

Are we still assumed to believe that being able to factorize a RSA number means a possible method of elimination, in that between for example 0 or 1 as a starting point and the number itself,
there could be numbers still left to factorize?

http://factordb.com/index.php?id=1100000000942499068

http://factordb.com/index.php?id=1100000000942711949

Above is one such example currently being worked on.

This pair becomes one of probably many such left before the factors are known for each and all.

Therefore the assumption is that those still remaining makes for the number in question still not factored at all.

Again that of the elimination method as mentioned above and next that of perhaps making a given or better guess, or perhaps assumption,
before trying out anything else.

Yafu, as you may know, includes the sqrt() function in order to make the square root of an integer number.

Do it the opposite way and the result becomes undesired or not being wished for, in that two or more factors are being returned, rather than a single one.

So, perhaps no point in that of addition or subtraction either, except for a couple of times.

I mentioned at BOINC a while ago that the factorization of the number in question perhaps may not be possible and still this question could be an open one.

Again, a couple of reasons for this being are being mentioned above.

The fact is that with the computer at my disposal, I did not find any relationship between the mentioned RSA-768 and other numbers which could be present.

Next I am not assuming or thinking that this in fact became loose numbers for which a documented method was being produced and distributed.

http://factordb.com/index.php?id=1100000000943449750

http://factordb.com/index.php?id=1100000000943536563

Apparently closing in a bit here now and could take the product here for the contining process.

storflyt32 · 2017-07-21, 22:02

Again, I think.

http://factordb.com/index.php?id=1100000000945120227

Here is a pretty good one when it comes to that of factors and also that the two at the end were not for the secret key this time, but rather an easy one.

http://factordb.com/index.php?id=1100000000948950482

http://factordb.com/index.php?id=1100000000948951746

Here a quite decent pair at the end which I got the factors for.

You are of course free of choice here, but also I could have some fun with this during the regular Friday evening show.

I have not made the weekend shopping yet, but chose to continue on this right now, because it became a P151 at the other end when also adding two other factors.

Next both keying it wrong first and also once again using the slingshot number on part of these gives me both a P112 and a P119 which I could add later.

Also the links for this could be added as well, because the C85 made for a quite good pair of factors.

http://factordb.com/index.php?id=1100000000949362774

http://factordb.com/index.php?id=1100000000949362788

Anyway, having the evening shift right now and possibly running into the night as well.

Here a pretty good pair, or perhaps rather set of factors for a number in question.

http://factordb.com/index.php?id=1100000000949362851

Continuing from the P86, it once again loops back at itself giving nothing new or more back in return.

http://factordb.com/index.php?id=1100000000949251085

I could next also test against the magic number here, but again could be a bit off (from the P86).

I will have the link shortly.

Next, stumbling here as well, because here there are a total of three factors, all which should be known.

Making a product of some three factors, among a total of four, also perhaps means which one to choose from such a selection.

Working on it, but the other, or remaining part, which has yet to be added, or posted, could be just as difficult.

http://factordb.com/index.php?id=1100000000949351047

Here it becomes a pair of P32 and P155 factors and could add to it here before getting to bed.

http://factordb.com/index.php?id=1100000000949532941

I will put it in the "to do" list for now, but the rear fan of the computer is not working and also the diods for the motherboard came off as well.

The power RESET button at the front does not work right now and I have to use the finger below the two graphics cards in order to turn on the computer.

I bought a new one, as you probably know and both this and also the other maintenance work, becomes the big task ahead when summer comes to an end and we could next sit together,
in order to carry out the work.

http://factordb.com/index.php?id=1100000000949341664

Also here meeting a dead end for now, but will let it run by means of ecm.

http://factordb.com/index.php?id=1100000000949351047

Adding here in the middle of the night, because if you happen to be a "numbermaniac", or at least one dealing with that of numbers, you in fact,
or actually could get the sense that it is not always about that of prime numbers versus composite numbers.

At least that is what I happened to notice and also that I am not a novice here either.

Yes, speaking of bit length, if you will and you could be having that of the RSA numbers for such a thing.

Next the sad fact that even the Mersenne prime number list, or list of factors, does not necessarily yield, or give for such a thing either.

As an example, I had a C52 during the day, which by recall had a P21 and a P32, or so.

Not that bad, but next that these are intermediate factors and far from what should be expected.

Next, if rather looking for that or such a thing which could be far fetched, it could end up far from sight, or perhaps estimated target or goal,
because this might not be what you are wishing for.

Factoring, as of today, or as it stands, is supposedly that of algorithms for such a purpose.

Still not perfect, it comes with a couple of flaws.

Except for that, I personally do not think or believe that a C200 should be factorized into a pair of P100 factors or so either.

Could it perhaps benefit science - yes, but if next that of possible validity - no.

Perhaps the reason for this is that we could still take that of Logic for granted and next expand it into that of numbers, in order to perhaps think that a couple of things might still not be feasible.

Again, if I did not mention it, stumbling here, because it ends up being some three and not four factors.

http://factordb.com/index.php?id=1100000000949351047

At least a quite good factorization here.

A P215, or perhaps P216, probably means nothing, by means of being of no significance at all, but what next about a given understanding?

Take it or leave it perhaps, but if I am not wrong, such a thing as Mersenneforum.org, or rather the way we are supposed to be finding new prime numbers,
at least could be based on an algorithm for such a thing and next perhaps also a given way of thinking.

If Charles Darwin was ever able to think about that of evolution as a subject, he probably also knew about both stepwise refinement and also stepwise thinking.

Yes, loopback, if you will and you could be having perhaps "tit-tat" a couple of times. while perhaps not so other times.

storflyt32 · 2017-08-09, 05:49

http://factordb.com/index.php?id=1100000000949341665

Here a nice one and this time by the server, because it is a difficult one.

Adding a bit more later on.

Like the following, which could be about the time it takes for a given factorization.

http://factordb.com/index.php?id=1100000000954075995

Total factoring time = 17887.5671 seconds

http://factordb.com/index.php?id=1100000000954236739

Total factoring time = 3656.9122 seconds

The first one should be the longest here and should be added first above, but the similar factors makes for a bit of confusion.

Working on it and when doing so and using cut and paste in order to get it fixed, the copied text being inserted makes the lines above (and not below this time) vanish, or disappear.

Next entering a carriage return and it again vanishes at the top, which makes me think that the line width of the buffer (top to bottom) could perhaps benefit from having one more line being added.

The second, or latter came in after the first one above and I did not think of any trial division before after a while, because it was in the middle of the day.

Except for that, I let it run to finish and also took a while for the second one as well.

Next it becomes a P131 twice, or in both results, adding to the confusion.

One thing to notice is that the first one came from the P131 (1161777693...<131>) which was already known, but then only with small factors being added.

So therefore the loopback at the P131 (1161...<131>) from the P131 of the first factorization (4772124691..<131>).

Always the comment at the end.

storflyt32 · 2017-08-11, 02:49

Needs a separate or new one right now, I think.

I was into a C83 earlier on, which because of a subsequent reboot and next restart of the computer, I lost the whole number.

Also making a note besides of that of a C84, which next became a pair of P42 factors.

Anyway, suggestions welcome here, because I am thinking of this one, because for now it is unfinished work.

Guess I am a supposed to be still polite.

http://factordb.com/index.php?id=1100000000954756277

Here it is a quite large factor when next doing it from a number meant for security purposes.

Only a P13 in between, but next takes a little while to factorize.

https://en.wikipedia.org/wiki/Perfect_number

What is a perfect number?

Should tell that the number 28 always came to mind when asking this question.

So perhaps 10 instead, because 10 = 2 * 5 ?

Or rather 10^33, because this number also goes by means of a name I came across today.

Perhaps mentioned here, but rather somewhere else, but I was also giving a thought about numbers as possible sets.

https://en.wikipedia.org/wiki/Set

Here for that of a start.

Regardless of it being 10, or 10^33, the first factor is always 2 and the next is supposed to be 5.

We make of both these numbers as being both prime numbers and also factors.

So I perhaps happened to call or nickname it the "Magic number" in the past, because it is supposedly "indivisible".

The general rule of thumb is that we choose to divide, or split such numbers up, in order to next make them rather divisable (or at least possibly so).

A composite number could be having a prime number or factor at "the other end", but here what next means such a thing as "the other end"?

Doing such a thing as factoring of numbers, it should be no secret that those numbers which could be so-called "RSA numbers", sometimes catches ones interest.

For now apparently no such thing as an official RSA-4096 number, but RSA-2048 is being left more or less guarded because of both a privacy and security issue, which in fact I
have come to respect.

The sad thing is that if such a thing as "make and break" could perhaps be true, we should know about both.

By means of making it, or such a thing rather that of sets instead, the whole thing could possibly be having another meaning.

From both a practical, as well as technological point of view, a PXXX could next multiply PYYY in order to make it CZZZ.

We probably are concerned with the fact that such a factorization is not possible from a just such a practical point of view, but what next about possible theory?

For now a little uncertain about the possible name here, but using such a factorization software like Yafu, a composite number with no direct factors could be having quite good factors in
between which still does not divide the number in question.

http://factordb.com/index.php?id=1100000000954812937

Example here, which should be a P54 which is already known.

Not necessarily about the software either, because I think it became quite good.

But rather a reporting issue, because I could perhaps be silly and next report "from my head".

Also that even such a thing might not be possible at times as well.

I have always thought of that of ecm as a means of doing a valid factorization of a number.

Question such a thing as LLR and I perhaps am not questioning any science, but perhaps that of numbers.

The fact is that I am not in the mood of posting such a thing as Mersenne semiprimes or the like here, because I lost the word for it.

But only that it actually, or in fact exist.

The main difference between the Mersenne primes and the Fermat factors, if you will, are both a possible difference in size and also their possible relationship.

Question such a thing as a Mersenne semiprime and you perhaps also could question the given method being used for such a thing.

Perhaps give a laugh about the whole thing, but I am still being reminded of the bus stop here.

I currently have a gigantic prime myself as my personal record.

One problem being noticed, or perhaps experienced, is that for now I find it hard at relating this number to something else which should be even larger,
because if so, this number should be a composite number.

Again back to that of sets as that of perhaps being of a programming issue.

A programming language like Pascal could at least be having the operators "+" "-" and "*", where each of these are not or NOT (forget the Logic here) arithmetic operators, or functions.

Again, that 10 and also 10^33 being mentioned at the top.

What if I tried factorizing 10^33?

Or am I perhaps getting it wrong here, because suddenly it was not that large anyway.

Therefore really not the point here, except for perhaps adding or subtracting 1 to the number.

P34 = 2237668761437315147090852353346777

P58 = 7627066397230573425374848252899760874164061612285621316223

P54 = 187204770770100083297887953100131286846649321750586503

For now, the P54 is only a loose factor here, but next also known.

If you do not mind, I would first try multiplying the P34 with the P54, before next doing anything more.

But if so, what happens next if you multilply all three factors with each other?

The result, at least should be a composite number.

So, which order of process, or in fact a given factorization next?

Am I perhaps supposed to be looking at a composite number at the other end, possibly even larger and next think that it perhaps or possibly could "divide"?

If perhaps doing so, it still could be possible factors in between, but if I forgot to mention it, it could also be that of "make and break" for such a thing as well.

I rather should finish it off before going to bed.

http://factordb.com/index.php?id=1100000000954812937

Anyway, the P54 should perhaps go here, but for now not successful.

Remainder is P39 = 850993544794824435316036738582698969211 and also already known.

The P54 versus the P58 should be left as an excersise for the possible user.

http://factordb.com/index.php?id=1100000000954820133

http://factordb.com/index.php?id=1100000000954820136

Becomes a nice finish of yet another quite good day.

http://factordb.com/index.php?id=1100000000954821388

Dangit, at least for now, because possible reporting could next make me a possible liar.

Give it a try, if you will.

http://factordb.com/index.php?id=1100000000954756255

http://factordb.com/index.php?id=1100000000954111417

The product of the two larger factors in each makes for a C141 and next quite heavy at the front.

Doing the flip-around from the larger number in question, it quickly becomes a P121 here, but I have not keyed in this yet.

http://factordb.com/index.php?id=1100000000956549861

http://factordb.com/index.php?id=1100000000956551754

I have the two remaining factors in the second link and will be adding shortly.

P67 = 3978642138166200436041214075494167204812101948690317652247717758073

P69 = 111111178760511010702681443211111111111112344186207010115067871111111

Adding the P67, but not for home use this time, because here it probably may not be done.

Adding both a P156 and a P167 to the Factor Database, but here the first of these became lost in the crowd and probably does not loop back at the P135.

I will have the dinner first and also the computer is experiencing a system hang right now.

http://factordb.com/index.php?id=1100000000956461136

http://factordb.com/index.php?id=1100000000956503835

Multiplying these two makes for both factors because here the factorization software allowed for this.

But next once again noticing the fact that while the C107 could need 179696 relations for its complete factorization, the C197 on the flip-around side will not do anymore either.

The explanation for this is not known, or unclear and at least the Magic number or the like is not based on the principle of square root of any numbers, or the Golden Ratio method.

https://en.wikipedia.org/wiki/Golden_ratio

First of all, how do you compute the bit length of a given number?

For a couple of these numbers, I choose to make them "dead angle" numbers, in that they will not meet or approach each other in a given way.

Make it perhaps easy one way and difficult the other way, or vice versa, but next that of P1 = 3 versus the Magic Number is not a good example either.

Better make a new one here.

storflyt32 · 2017-08-19, 12:10

http://factordb.com/index.php?id=1100000000956564228

http://factordb.com/index.php?id=1100000000956565023

Here a bit interesting, because I noted down the loose factors for the C116.

The C189 on the other hand, has a P21, P34 and P135 as its three factors and next continuing on the C116, in order to get it right.

Factors coming up shortly but also it should be a flip-around for the P135 as well, which should be different than the one previously mentioned.

http://factordb.com/index.php?id=1100000000956576336

http://factordb.com/index.php?id=1100000000956014448

And next perhaps bit of a strange or goofy thing, because I went for the first of the last beers remaining in the fridge and will soon be off.

Adding the P30 in the second link for possible completeness.

Am I not wrong, but is not there such a thing as factor dependency, or perhaps interdependency when it comes to these numbers?

Depending on both size of factors and also their relative difference within a factorization and also that there are many of them as well, how far are we still off when it comes to this?

Is it possible to give an answer here?

Suggestions welcome.

The C189 is having a P42 and as thought, a bit more easy than the C107 which still has one hour or two left.

This should be because of both the preceding factors, as well as the initial starting point, or reference on each side, which should differ for each such number.

My guess is that it could be getting more difficult, because you are progressing in towards the center, but next a valid factorizaton of a C180 into two P90 factors could be yet another issue.

storflyt32 · 2017-08-31, 09:13

http://factordb.com/index.php?id=1100000000964713629

Adding here when on 32 bits, but perhaps not in correct order, because I had a break right now.

Also a P147 in my list as well.

http://factordb.com/index.php?id=1100000000964955877

Total factoring time = 4452.6960 seconds

Initially a PRP99 before the final output, so no big secret here, because currently running on a 32 bits partition because of a software installation failure.

A new computer being turned on today for the first time and doing quite well on the motherboard and graphics card, but for now unable to connect with a monitor because of a connector mismatch.

Also two more disks lying on the shelf for possible use, so it bit of excitement around right now.

I will be checking the two factors later on, but my guess is that we are closing in a little here.

http://factordb.com/index.php?id=1100000000965087791

http://factordb.com/index.php?id=1100000000965089453

Here a quite good factor in the first link, considering the size of the whole number.

Continuing, it becomes the same P17 in both, but need to do the shopping first and also that I am on a 32 bits partition for now.

At least I know the name for this, namely semiprime and also its intended function or purpose.

Again the cup of coffee for this as well, because I am not supposed to be cheating either, because in fact I have a couple such being stored away.

Right now experiencing a problem with that of editing, because having two or more different e-mail accounts, each lies in separate tabs and when next using Notepad as well, I am losing track of it
despite a possible draft for some of these things, at least when it comes to that of e-mail.

If this is because of a recent Windows update, it is not working very well with me and perhaps needs a closer look.

The problem is that it is not worth wasting 300 KB of space here only for a given example, so here it becomes only a similar comparison for that of shorter, or "feasible" numbers.

Two recent factorizations gave me a composite number when multiplying the two larger factors in each and next flipping around, it becomes a P149 factor.

Not reported yet at all, but will be doing so coming up.

Only goes or comes to show that perhaps cheating in such a way as mentioned above could also return possible results.

The computer being turned on for the first time earlier today could perhaps be able to factorize one number which I think could be a RSA-512 number.

Starting with the four digits 9712... from my recall, it could be more difficult than RSA-155, so here a quite good example.

But first I will need a Windows installation or setup and for this I will probably go for Windows 10.

Now I suddenly found the other tab for this and next it becomes something else.

Doing a cut and paste below and will edit it later.

storflyt32 · 2017-09-01, 18:11

Next at least I know the name for this, namely semiprime and also its intended function or purpose.

Again the cup of coffee for this as well, because I am not supposed to be cheating either, because in fact I have a couple such being stored away and again you need to
know the intended purpose or meaning, because "*" or "x" (small or large caps) is the multiplication symbol and "/" is the division symbol.

Next perhaps needs the correct translation, because in my native language, it translates into divisor and dividend, respectively.

https://en.wikipedia.org/wiki/Dividend

https://en.wikipedia.org/wiki/Division_(mathematics)

https://en.wikipedia.org/wiki/Divisor

Notice the ambiguation here for the first term, but if I make it 1/7, here 1 should be the possible dividend by means of Mathematics and not any Finance, in the same way as 7 should be the divisor.

Suggestions welcome, but will make a fix here.

Becomes like that of div and mod for that of integer numbers ("%" when using Yafu) and now my edit disappeared, or vanished.

And no need for any draft here since I am lucky to edit my own stuff.

The reason for this is the mentioned semiprime or semiprimes and the possible need, or even lack of it becomes to that of possible cheating.

If any such, I have never seen a discussion of this and next it should not be about the Scientific Method, or the Method of Proof here either for this.

I will do the weekend shopping first, but it could next be split in two parts or halves here as well.

I will keep the line above for now, but next did the shopping and are looking for the rest of it.

More technically speaking, a RSA number is probably not having any syntax at all.

Therefore one set for that of Mersenne prime numbers and also possible factors (2^61-1) and (2^89-1).

Is it possible to value a prime number or factor against another when it comes to type, except for being perhaps Mersenne, Fermat, or possibly rep-digit?

If I multiply all the Mersenne factors up to a reasonable size (Mersenne23 or less), I could get a decent composite number, but next I do not think that
C46 = 1427247692705959880439315947500961989719490561 is such a RSA number either.

http://factordb.com/index.php?id=1100000000193090724

This because if so, it has to be specifically designated as such and one reason is the possible bit length of the composite number.

Press the More information button here and for the 4246 digit number in the middle, we have a quite good 4182 digit prime.

The only reason you sometimes know for that or such for even larger numbers is because you choose to multiply those numbers.

http://factordb.com/index.php?id=1100000000964936507

http://factordb.com/index.php?id=1100000000964928845

http://factordb.com/index.php?id=1100000000964928928

Here now three good examples for this, because I added one in the middle and next that these are not easy ones, at least not with 32 bits, running overnight using ecm and still not finished.

You are welcome at giving a try, because here no problem with me.

Next that this could become a double semiprime of sorts by means of multiplying, or product and could relate to an even bigger number with their respective factors the usual way.

Because this is supposed to be about factoring, you also should know in which way it is supposed to be working.

A good example is 2 versus 3, or 3 versus 5, because here it becomes either 0.66666...., or 1.66667 if I am not missing something.

Next make it an integer number for at least the latter and add a million "6" digits before the final "7".

Unable to do it right now, I sometimes am having fun when on a 64 bit partition and next I may possibly get access to another second one in spare.

I will be counting my disks later on and will give you a rough number, but for now it became mostly Windows XP here, making for a big problem.

Again no point of listing a million digits here, so rather about a given Methodology and this time for that of numbers and not necessarily any science.

https://en.wikipedia.org/wiki/Methodology

You perhaps know that I perhaps gave mentioning of that of numbers being "poor man's science".

In order not to insult anyone, I will perhaps refrain from that, but rather there could still be a possible difference.

Getting back at it when I have read the article.

Because of the possible limits of factorization, I checked with the msieve application, which for now is a .zip file, but also 64 bits only.

I will return back to this when the other computer is up and working.

Only that a given C313 or C314 (needs checking) could be having a P156 and a P157 as its possible factors and here we are back to that above.

But for now only being aware of the possible limits of factoring and not necessarily "as is" in one given way or another.

Checking with the edit for this later on.

storflyt32 · 2017-09-01, 18:55

One thing of possible concern, or at least thinking about, is the possible "superhighway" of prime numbers which possibly could be there.

Many numbers still remain to be factorized, like that of RSA-1024 and RSA-2048.

Either they are at least semiprimes, or possibly RSA numbers, but if together with family of friends, it could end up being 2, 3, 5, 7 and so on and next not much more.

The reason why at least RSA-256 is no problem today and RSA-512 could be factored at times, is no excuse for the fact that the number of possible factors in total could be very large.

RSA-1024 is not possible to factor directly, so here another example.

First of all, this has not been keyed in yet, so please if you could skip this for now, I would be very glad or happy, because this became a sequence and having it keyed in in a proper order, could make for both me and others feeling better.

P40 = 1206141817390868369904697458937941898139

P89 = 15316861479442889529311995789441719383377177013171568971730011284995339928476982696581569

Becomes a C128 as the product here and probably possible to factor using msieve.

Next try the C128 from RSA-1024 (the Magic Number) and you get the P149 with a little in between.

http://factordb.com/index.php?query=%282%5E48853-1%29

My favorite above, except for perhaps the syntax, but should read (2^48853-1).

Here the P1764 became my first better find or discovery and working hard here, it mostly sorted out.

The remaining C12593 is a "beast" of a number and perhaps not doable at all, even with a new computer soon ready.

My current record is not the P1764, however, but rather a PRP12576, which is a gigantic prime and also that there is a 17 digit difference from the C12593 above.

I happen to know that the P1764 and PRP12576 are related with each other in one way or another, but which one, or how, I really do not know.

Next that I also know that it does not divide the other way either, even when making the C48853 twice, or four times as large in size.

You always make it 210 for that of 2 * 3 * 5 * 7, but next "what next" in such a sequence when a possible relationship between numbers is not directly available or present?

I definitely know that regular sieving is one possible option or alternative for finding prime numbers, but perhaps not the perfect solution either,
because a 321 number or Cullen/Woodall number always needs to be processed by means of LLR.

My guess is that the P1764 and next the PRP12576 could theoretically be making the next number in the sequence a possible megaprime, but here I would like to ask for a
possible way of getting at such a number.

Because the PRP12576 is not readily available or in front of me (I could be checking in with BOINC for this), I do not have it right now.

But only that I mentioned the fact earlier on my possible guess or suspicion that it could go straight up for some of the factors in a sequence and next I did not know the way in which to proceed.

storflyt32 · 2017-10-15, 05:53

Continuing on a Windows, 32 bit partition right now, because of a bit of problems being experienced.

Also need ticking the stay logged in box here in order to keep the current session, so now this was done as well.

http://factordb.com/index.php?id=1100000001053969348

http://factordb.com/index.php?id=1100000001053969978

P64 = 6521004766994961131998652758478623734567850934300959187999440927

P72 = 132630796754188196686159842513385353980595967923227514053572714567610003

Here both are end factors from two different factorizations, multiplied with each other.

Not that unusual perhaps, but here both slightly easier and also slightly better as well.

http://factordb.com/index.php?id=1100000001054063735

http://factordb.com/index.php?id=1100000001054062880

The second link above has a pair of P40 and P96 factors and next took some four hours on Windows, 32 bits.

Initially a PRP96 here, except for perhaps the dinner in the meantime.

The second was started only a couple of minutes before, so here no factors yet.

Returning back to the desktop, apparently more easier here, because the word or phrase "either / or", could sometimes be part of Logic,
but next also which one should come first, or be better.

Also when editing that above, for some reason I had become logged out and therefore made it impossible to post.

A little bit of unusual perhaps, but at least now I know when it happens.

Here a pair of P26 and P129 factors, respectively and perhaps could be added first when having the early dinner put away.

Also that here it took 3 minutes and 30 seconds only.

But except for that, the first pair is a pretty good one here and I will have it in a short time.

But rather becoming a bit confused that only a C99 makes for a bit of a show, or at least juggling, by walking through the complex process of echoing lines like

"Bpoly 3484 of 4096: buffered 538 rels, checked 105253 (8.95 rels/sec)" to the screen in successive or repeating order.

Taking a long time as well, here perhaps yet another example of factors which could be sometimes individually known, but when next multiplied, it makes for such complexity.

Perhaps not directly stated, but we may eventually find ourselves in a situation where we need to know each small part or step of the whole road, leaving nothing in between, or left.

If I ever asked myself what is on the "other side" of that of the Magic number (RSA-1024) and the larger cousin RSA-2048 and next the fact that it does not divide here, but only becomes smaller factors.

So here not a good example at all, but also that a P153 was being found earlier today from doing it the opposite way, namely by means of multiplication and next the regular thing.

http://mathforum.org/kb/message.jspa?messageID=7890114

Here a quite good example of such factorization which is next some 5 years old, but is perhaps known.

Except for that, possibly will need to break off a little in order to not disappoint those in charge of running the projects under BOINC and their respective deadlines.

Perhaps needs a bit more editing above, because it became a little bit of butter on bread here.

storflyt32 · 2017-10-15, 14:49

Here a bit of surprise right now and also a good reason to quit for the day.

Ending up with a P260 in my factorizations, checking with RSA-2048 first, which is not making for any good.

Next the C1133 of (2^4096+1) which of course is Fermat, but here apparently a PRP871 the other way, with only factors 2^3 and 7 in between.

Anyone better here, because I do not recall such a thing myself either.

Just in the door, I could perhaps have it later on at a better time and also could be of interest for the larger Fermat numbers as well.

Continuing here, but some good news right now.

Finding or getting across a P60 today, where the other factor is a P13, the first is a pretty nice one and next trying out with the well-known C147 Aliquot sequence number.

http://factordb.com/index.php?id=1100000000633991051

Here getting P1 = 5, both ways in between, for some two factors, the other a P87, but next that I have not reported it yet.

Apparently closing in here right now, because the other way around could be even more difficult.

http://factordb.com/index.php?id=1100000001061898387

Edit: Together with the Friday beer, giving it a try here as well.

Apparently a P25 or so at first and next I will let it go, or continue.

Because here or next some other stuff as well, taking up a bit, or if not considerable amount of time and next also I am also proud as well.

I will have this one also shortly, except for perhaps not being a better one.

Edit: Could add that I lost a P166 right now, because the computer went into a freeze and became unresponsible, needing a restart.

Here also a pretty nice looking number as well, so a bit of shame when it happens.

It should be the mentioned undervolt problem here and right now my CUDA tasks for the two projects are not running.

Next the P50 from the C147 Aliquot sequence number and at first an even number here before next continuing.

http://factordb.com/index.php?id=1100000001062276468

Eventually getting it sorted and next having the P50 here.

http://factordb.com/index.php?id=1100000001062280638

Also that this could also be work in progress as well, so next also that above for both the P22 and the P68.

If next continuing, perhaps something else or different, because this time again flipping around and next for something a bit larger.

http://factordb.com/index.php?id=1100000001062282513

Here adding both the P13 and also the P21 when first starting up with C11 = 14807725969 (or 121687 * 121687) .

But again that both prime numbers and also factors for such could be telling about a possible weighted distribution of such numbers when looked at or viewed in a larger context,
except for sometimes making them more or less equal in size, if not even comparing their individual sizes against each other and also their possible relationship.

Giving the above a thought, perhaps.

http://factordb.com/index.php?id=1100000001062284241

Here adding a P22 as well and it becomes a loop or cycle of sorts, because I could be back at a previous found factor once again.

But next that even a piece of cake does not help right now and therefore needs a bit more of thinking.

Next doing so and the P22 apparently is a common divisor among two different numbers, leaving only the P50 and P68 here.

http://factordb.com/index.php?id=1100000001062280639

http://factordb.com/index.php?id=1100000001062284242

Therefore the flip around is needed here for possibly anything more and will have it in a short while.

http://factordb.com/index.php?id=1100000001062286920

http://factordb.com/index.php?id=1100000001062287002

Again it apparently works out quite well, except for perhaps making a guess for the C117 in the first link above.

http://factordb.com/index.php?id=1100000001062288152

Here making perhaps an unneeded entry because I could be still sleeping, so my apologies for that.

But rather that the C117 could be multiplied with such a number as RSA-155 and next taking the square root.

Here a P20 for this which will be added in a moment, but next should be the same flip around in order for possibly even more.

Perhaps time for making a new one here, but before I go for tonight, again being a bit more brave and next adding a P141 to my list.

The PXXX of numbers, where at least the first X should start or begin with that of 1 as a digit, is perhaps kind of a motorway, if perhaps not any superhighway either.

I mentioned the falling leaf a couple of other places and also the context in which such a thing should belong.

The YouTube video being around and next about such a thing as numbers, could be telling about both such a tree for such numbers and also their weighted distribution, if not any
relationship as well, as mentioned above.

The larger you get for that of the size of such numbers, that of Probability and here Number probability, should perhaps be telling about such a possible distribution.

https://en.wikipedia.org/wiki/Probability_distribution

Should there be more large prime numbers than those factors which could be small, only because of their size, or is it perhaps vice versa, or the opposite way around?

https://en.wikipedia.org/wiki/Mersenne_prime

Next reading the footnotes, some four in all, after the List of known Mersenne primes a little down the page.

The links above should be in the opposite order, but getting back at this tomorrow.

But only that a bit of a gap could be visible between at least M48 and M49 here, except for making no guess or even notice that such a number like P1 = 127 is supposed to be a Genefer factor.

Or perhaps I am wrong here?

Checking with this tomorrow, because for now it became late night here, but for now at least not in the list of large prime numbers for the latter.

2017-07-01, 04:45	#45
storflyt32 Feb 2013 2²×5³ Posts	Making a new one here. http://factordb.com/index.php?id=1100000000938270361 http://factordb.com/index.php?id=1100000000938278465 The C77, because it is still two factors, but next fully factored, I think was done on the server. The C195 at the other end next is having a quite good factor as well, namely a P49, which could be added. Still a C146 to go here though, so not yet finished here. A couple of other factors as well in my list, which could be added first. This when keying in n!-1 and n!+1 in the FDB, which is relating to that of Factorial numbers. Here a little bit in the dark on the subject, but both Factorial numbers and Primorial numbers are part of the Project Staging Area at PrimeGrid. The pocket calculator could be able to come up with 69! before unable to do any more, but next it becomes even at the end, before either subtracting or adding. As usual not all the odd numbers being returned are prime either, but for each of these types we apparently are having record primes. Perhaps a little more could be done with those numbers which are only composite or factors here, because finding anything larger could be a difficult thing. Another thing, I happened to be something funny before signing off yesterday. For that of Astronomy as a subject, we could be having the Arecibo message in our lists, or perhaps memory. And here about a message being broadcast from Earth towards a globular cluster and not something that was picked up. Making it a binary output or representation, it becomes some 23 lines and 79 columns of the whole message. I chose to remove or omit the starting 0's and next used copy and paste in order to copy part of the output to Notepad. Ending on a single line, with a couple of 1's in consecutive order at the end, the number, when being thought of as decimal such, is having factor P1 = 3 and the remaining number a rep-digit factor or prime, some 300 - 400 digits or so. Only to have it mentioned, because I am finishing off the rest of the beer right now, but could have it tomorrow. So, while still having fun, of course keying it wrong and it becomes a P59 at the end. http://factordb.com/index.php?id=1100000000938435249 http://factordb.com/index.php?id=1100000000938435263 P49 = 6384627520682549821072782803042294957487643979279 P59 = 24805184834556493674296971841383950146529962250161488466941 Both factors are known, but except for keying it wrong, also luck perhaps were striking back here as well. http://factordb.com/index.php?id=1100000000938509033 Also mentioning a possible overcommitment at other places, but here not difficult at all, when next excluding the P14. Total factoring time = 2938.1431 seconds Having the coffee and cake shortly before 11:30 AM in the morning, because I sat the night over, I keyed in both n!-1 and n!+1 in the FDB for their respective outputs. But if next doing the same related to the possible factorizations of RSA numbers, particularly those already known, my guess is that there is no similar syntax here. http://factordb.com/index.php?id=1100000000937794539 Continuing here right now, because it could be an adjacent run, or factorization corresponding to this number. Next needs checking, but as previously mentioned, got slightly overcommitted right now and experiencing a bit of difficulty. http://factordb.com/index.php?id=1100000000938599206 http://factordb.com/index.php?id=1100000000938599225 Making it a new session here as well, here became a triple pair or set of factors which were not that difficult. Total factoring time = 647.1420 seconds The first one becomes a loose pair of P40 and P54 factors from my list and if you wish, you may give it a try. Except for that, I could put these factors up here a bit later on. Also that when looking at the results, the P38 and P50 pair of factors is definitely a quite nice pair from its appearance. Also checking in with that funny looking C174, it now is at 600/7553 curves after finishing off both 2350 and 4480 curves first. Either it becomes a restart first, but for now ETA is listed as 375.71 hours here and perhaps or probably will not succeed. Now at 703/7553 curves and still running, ETA is now being given as 369.01 hours. Also giving a try on the C145 in the middle, but here it could take some 6 more hours. Last fiddled with by storflyt32 on 2018-07-26 at 22:58

2017-07-07, 00:37	#46
storflyt32 Feb 2013 2²×5³ Posts	http://factordb.com/index.php?id=1100000000939236158 I could end up repeating myself because of having an Edit box open and next adding contents where it already may have been posted. I will try to avoid it, but if so, I could edit it away later on if it happens. But here an example of something neither easy or directly hard, but rather something in between, at least when it comes to my own computer. I needed a break a short while ago and for now have not continued with the session, except for adding three more P100+ factors, without continuing from there. And also it mostly blew right now, because it became a restart of the computer which I tried to abort, but next it turned or shut off without warning. Back again after shuffling my equipment in the living room, because here it becomes a purchase of a second computer and also a quite powerful one. So rather I gave the following a thought. RSA-768 as you may know, is a 232 digit composite number having two P116 factors. If I was unable to use the hard switch or button on this number, we probably could be having the discussion about cracking of numbers, or the similar, where For now lacking the proper word or syntax which should be used here, but a similar discussion could be that of RSA numbers versus possible encryption, meaning cryptography. Again, I am not into that subject, but still give a thought of the way a given number is supposed to be "cracked". I prefer to make it that of numbers only, but still was able to come up with a name for such a number. Are we still assumed to believe that being able to factorize a RSA number means a possible method of elimination, in that between for example 0 or 1 as a starting point and the number itself, there could be numbers still left to factorize? http://factordb.com/index.php?id=1100000000942499068 http://factordb.com/index.php?id=1100000000942711949 Above is one such example currently being worked on. This pair becomes one of probably many such left before the factors are known for each and all. Therefore the assumption is that those still remaining makes for the number in question still not factored at all. Again that of the elimination method as mentioned above and next that of perhaps making a given or better guess, or perhaps assumption, before trying out anything else. Yafu, as you may know, includes the sqrt() function in order to make the square root of an integer number. Do it the opposite way and the result becomes undesired or not being wished for, in that two or more factors are being returned, rather than a single one. So, perhaps no point in that of addition or subtraction either, except for a couple of times. I mentioned at BOINC a while ago that the factorization of the number in question perhaps may not be possible and still this question could be an open one. Again, a couple of reasons for this being are being mentioned above. The fact is that with the computer at my disposal, I did not find any relationship between the mentioned RSA-768 and other numbers which could be present. Next I am not assuming or thinking that this in fact became loose numbers for which a documented method was being produced and distributed. http://factordb.com/index.php?id=1100000000943449750 http://factordb.com/index.php?id=1100000000943536563 Apparently closing in a bit here now and could take the product here for the contining process. Last fiddled with by storflyt32 on 2017-07-23 at 03:47

2017-07-21, 22:02	#47
storflyt32 Feb 2013 2²·5³ Posts	Again, I think. http://factordb.com/index.php?id=1100000000945120227 Here is a pretty good one when it comes to that of factors and also that the two at the end were not for the secret key this time, but rather an easy one. http://factordb.com/index.php?id=1100000000948950482 http://factordb.com/index.php?id=1100000000948951746 Here a quite decent pair at the end which I got the factors for. You are of course free of choice here, but also I could have some fun with this during the regular Friday evening show. I have not made the weekend shopping yet, but chose to continue on this right now, because it became a P151 at the other end when also adding two other factors. Next both keying it wrong first and also once again using the slingshot number on part of these gives me both a P112 and a P119 which I could add later. Also the links for this could be added as well, because the C85 made for a quite good pair of factors. http://factordb.com/index.php?id=1100000000949362774 http://factordb.com/index.php?id=1100000000949362788 Anyway, having the evening shift right now and possibly running into the night as well. Here a pretty good pair, or perhaps rather set of factors for a number in question. http://factordb.com/index.php?id=1100000000949362851 Continuing from the P86, it once again loops back at itself giving nothing new or more back in return. http://factordb.com/index.php?id=1100000000949251085 I could next also test against the magic number here, but again could be a bit off (from the P86). I will have the link shortly. Next, stumbling here as well, because here there are a total of three factors, all which should be known. Making a product of some three factors, among a total of four, also perhaps means which one to choose from such a selection. Working on it, but the other, or remaining part, which has yet to be added, or posted, could be just as difficult. http://factordb.com/index.php?id=1100000000949351047 Here it becomes a pair of P32 and P155 factors and could add to it here before getting to bed. http://factordb.com/index.php?id=1100000000949532941 I will put it in the "to do" list for now, but the rear fan of the computer is not working and also the diods for the motherboard came off as well. The power RESET button at the front does not work right now and I have to use the finger below the two graphics cards in order to turn on the computer. I bought a new one, as you probably know and both this and also the other maintenance work, becomes the big task ahead when summer comes to an end and we could next sit together, in order to carry out the work. http://factordb.com/index.php?id=1100000000949341664 Also here meeting a dead end for now, but will let it run by means of ecm. http://factordb.com/index.php?id=1100000000949351047 Adding here in the middle of the night, because if you happen to be a "numbermaniac", or at least one dealing with that of numbers, you in fact, or actually could get the sense that it is not always about that of prime numbers versus composite numbers. At least that is what I happened to notice and also that I am not a novice here either. Yes, speaking of bit length, if you will and you could be having that of the RSA numbers for such a thing. Next the sad fact that even the Mersenne prime number list, or list of factors, does not necessarily yield, or give for such a thing either. As an example, I had a C52 during the day, which by recall had a P21 and a P32, or so. Not that bad, but next that these are intermediate factors and far from what should be expected. Next, if rather looking for that or such a thing which could be far fetched, it could end up far from sight, or perhaps estimated target or goal, because this might not be what you are wishing for. Factoring, as of today, or as it stands, is supposedly that of algorithms for such a purpose. Still not perfect, it comes with a couple of flaws. Except for that, I personally do not think or believe that a C200 should be factorized into a pair of P100 factors or so either. Could it perhaps benefit science - yes, but if next that of possible validity - no. Perhaps the reason for this is that we could still take that of Logic for granted and next expand it into that of numbers, in order to perhaps think that a couple of things might still not be feasible. Again, if I did not mention it, stumbling here, because it ends up being some three and not four factors. http://factordb.com/index.php?id=1100000000949351047 At least a quite good factorization here. A P215, or perhaps P216, probably means nothing, by means of being of no significance at all, but what next about a given understanding? Take it or leave it perhaps, but if I am not wrong, such a thing as Mersenneforum.org, or rather the way we are supposed to be finding new prime numbers, at least could be based on an algorithm for such a thing and next perhaps also a given way of thinking. If Charles Darwin was ever able to think about that of evolution as a subject, he probably also knew about both stepwise refinement and also stepwise thinking. Yes, loopback, if you will and you could be having perhaps "tit-tat" a couple of times. while perhaps not so other times. Last fiddled with by storflyt32 on 2017-08-09 at 05:49

2017-08-09, 05:49	#48
storflyt32 Feb 2013 2²×5³ Posts	http://factordb.com/index.php?id=1100000000949341665 Here a nice one and this time by the server, because it is a difficult one. Adding a bit more later on. Like the following, which could be about the time it takes for a given factorization. http://factordb.com/index.php?id=1100000000954075995 Total factoring time = 17887.5671 seconds http://factordb.com/index.php?id=1100000000954236739 Total factoring time = 3656.9122 seconds The first one should be the longest here and should be added first above, but the similar factors makes for a bit of confusion. Working on it and when doing so and using cut and paste in order to get it fixed, the copied text being inserted makes the lines above (and not below this time) vanish, or disappear. Next entering a carriage return and it again vanishes at the top, which makes me think that the line width of the buffer (top to bottom) could perhaps benefit from having one more line being added. The second, or latter came in after the first one above and I did not think of any trial division before after a while, because it was in the middle of the day. Except for that, I let it run to finish and also took a while for the second one as well. Next it becomes a P131 twice, or in both results, adding to the confusion. One thing to notice is that the first one came from the P131 (1161777693...<131>) which was already known, but then only with small factors being added. So therefore the loopback at the P131 (1161...<131>) from the P131 of the first factorization (4772124691..<131>). Always the comment at the end. Last fiddled with by storflyt32 on 2017-08-11 at 02:55

2017-08-11, 02:49	#49
storflyt32 Feb 2013 2²×5³ Posts	Needs a separate or new one right now, I think. I was into a C83 earlier on, which because of a subsequent reboot and next restart of the computer, I lost the whole number. Also making a note besides of that of a C84, which next became a pair of P42 factors. Anyway, suggestions welcome here, because I am thinking of this one, because for now it is unfinished work. Guess I am a supposed to be still polite. http://factordb.com/index.php?id=1100000000954756277 Here it is a quite large factor when next doing it from a number meant for security purposes. Only a P13 in between, but next takes a little while to factorize. https://en.wikipedia.org/wiki/Perfect_number What is a perfect number? Should tell that the number 28 always came to mind when asking this question. So perhaps 10 instead, because 10 = 2 * 5 ? Or rather 10^33, because this number also goes by means of a name I came across today. Perhaps mentioned here, but rather somewhere else, but I was also giving a thought about numbers as possible sets. https://en.wikipedia.org/wiki/Set Here for that of a start. Regardless of it being 10, or 10^33, the first factor is always 2 and the next is supposed to be 5. We make of both these numbers as being both prime numbers and also factors. So I perhaps happened to call or nickname it the "Magic number" in the past, because it is supposedly "indivisible". The general rule of thumb is that we choose to divide, or split such numbers up, in order to next make them rather divisable (or at least possibly so). A composite number could be having a prime number or factor at "the other end", but here what next means such a thing as "the other end"? Doing such a thing as factoring of numbers, it should be no secret that those numbers which could be so-called "RSA numbers", sometimes catches ones interest. For now apparently no such thing as an official RSA-4096 number, but RSA-2048 is being left more or less guarded because of both a privacy and security issue, which in fact I have come to respect. The sad thing is that if such a thing as "make and break" could perhaps be true, we should know about both. By means of making it, or such a thing rather that of sets instead, the whole thing could possibly be having another meaning. From both a practical, as well as technological point of view, a PXXX could next multiply PYYY in order to make it CZZZ. We probably are concerned with the fact that such a factorization is not possible from a just such a practical point of view, but what next about possible theory? For now a little uncertain about the possible name here, but using such a factorization software like Yafu, a composite number with no direct factors could be having quite good factors in between which still does not divide the number in question. http://factordb.com/index.php?id=1100000000954812937 Example here, which should be a P54 which is already known. Not necessarily about the software either, because I think it became quite good. But rather a reporting issue, because I could perhaps be silly and next report "from my head". Also that even such a thing might not be possible at times as well. I have always thought of that of ecm as a means of doing a valid factorization of a number. Question such a thing as LLR and I perhaps am not questioning any science, but perhaps that of numbers. The fact is that I am not in the mood of posting such a thing as Mersenne semiprimes or the like here, because I lost the word for it. But only that it actually, or in fact exist. The main difference between the Mersenne primes and the Fermat factors, if you will, are both a possible difference in size and also their possible relationship. Question such a thing as a Mersenne semiprime and you perhaps also could question the given method being used for such a thing. Perhaps give a laugh about the whole thing, but I am still being reminded of the bus stop here. I currently have a gigantic prime myself as my personal record. One problem being noticed, or perhaps experienced, is that for now I find it hard at relating this number to something else which should be even larger, because if so, this number should be a composite number. Again back to that of sets as that of perhaps being of a programming issue. A programming language like Pascal could at least be having the operators "+" "-" and "", where each of these are not or NOT (forget the Logic here) arithmetic operators, or functions. Again, that 10 and also 10^33 being mentioned at the top. What if I tried factorizing 10^33? Or am I perhaps getting it wrong here, because suddenly it was not that large anyway. Therefore really not the point here, except for perhaps adding or subtracting 1 to the number. P34 = 2237668761437315147090852353346777 P58 = 7627066397230573425374848252899760874164061612285621316223 P54 = 187204770770100083297887953100131286846649321750586503 For now, the P54 is only a loose factor here, but next also known. If you do not mind, I would first try multiplying the P34 with the P54, before next doing anything more. But if so, what happens next if you multilply all three factors with each other? The result, at least should be a composite number. So, which order of process, or in fact a given factorization next? Am I perhaps supposed to be looking at a composite number at the other end, possibly even larger and next think that it perhaps or possibly could "divide"? If perhaps doing so, it still could be possible factors in between, but if I forgot to mention it, it could also be that of "make and break" for such a thing as well. I rather should finish it off before going to bed. http://factordb.com/index.php?id=1100000000954812937 Anyway, the P54 should perhaps go here, but for now not successful. Remainder is P39 = 850993544794824435316036738582698969211 and also already known. The P54 versus the P58 should be left as an excersise for the possible user. http://factordb.com/index.php?id=1100000000954820133 http://factordb.com/index.php?id=1100000000954820136 Becomes a nice finish of yet another quite good day. http://factordb.com/index.php?id=1100000000954821388 Dangit, at least for now, because possible reporting could next make me a possible liar. Give it a try, if you will. http://factordb.com/index.php?id=1100000000954756255 http://factordb.com/index.php?id=1100000000954111417 The product of the two larger factors in each makes for a C141 and next quite heavy at the front. Doing the flip-around from the larger number in question, it quickly becomes a P121 here, but I have not keyed in this yet. http://factordb.com/index.php?id=1100000000956549861 http://factordb.com/index.php?id=1100000000956551754 I have the two remaining factors in the second link and will be adding shortly. P67 = 3978642138166200436041214075494167204812101948690317652247717758073 P69 = 111111178760511010702681443211111111111112344186207010115067871111111 Adding the P67, but not for home use this time, because here it probably may not be done. Adding both a P156 and a P167 to the Factor Database, but here the first of these became lost in the crowd and probably does not loop back at the P135. I will have the dinner first and also the computer is experiencing a system hang right now. http://factordb.com/index.php?id=1100000000956461136 http://factordb.com/index.php?id=1100000000956503835 Multiplying these two makes for both factors because here the factorization software allowed for this. But next once again noticing the fact that while the C107 could need 179696 relations for its complete factorization, the C197 on the flip-around side will not do anymore either. The explanation for this is not known, or unclear and at least the Magic number or the like is not based on the principle of square root of any numbers, or the Golden Ratio method. https://en.wikipedia.org/wiki/Golden_ratio First of all, how do you compute the bit length of a given number? For a couple of these numbers, I choose to make them "dead angle" numbers, in that they will not meet or approach each other in a given way. Make it perhaps easy one way and difficult the other way, or vice versa, but next that of P1 = 3 versus the Magic Number is not a good example either. Better make a new one here. Last fiddled with by storflyt32 on 2017-08-19 at 20:52*

2017-08-19, 12:10	#50
storflyt32 Feb 2013 2²·5³ Posts	http://factordb.com/index.php?id=1100000000956564228 http://factordb.com/index.php?id=1100000000956565023 Here a bit interesting, because I noted down the loose factors for the C116. The C189 on the other hand, has a P21, P34 and P135 as its three factors and next continuing on the C116, in order to get it right. Factors coming up shortly but also it should be a flip-around for the P135 as well, which should be different than the one previously mentioned. http://factordb.com/index.php?id=1100000000956576336 http://factordb.com/index.php?id=1100000000956014448 And next perhaps bit of a strange or goofy thing, because I went for the first of the last beers remaining in the fridge and will soon be off. Adding the P30 in the second link for possible completeness. Am I not wrong, but is not there such a thing as factor dependency, or perhaps interdependency when it comes to these numbers? Depending on both size of factors and also their relative difference within a factorization and also that there are many of them as well, how far are we still off when it comes to this? Is it possible to give an answer here? Suggestions welcome. The C189 is having a P42 and as thought, a bit more easy than the C107 which still has one hour or two left. This should be because of both the preceding factors, as well as the initial starting point, or reference on each side, which should differ for each such number. My guess is that it could be getting more difficult, because you are progressing in towards the center, but next a valid factorizaton of a C180 into two P90 factors could be yet another issue. Last fiddled with by storflyt32 on 2017-08-22 at 14:31

2017-08-31, 09:13	#51
storflyt32 Feb 2013 2²×5³ Posts	http://factordb.com/index.php?id=1100000000964713629 Adding here when on 32 bits, but perhaps not in correct order, because I had a break right now. Also a P147 in my list as well. http://factordb.com/index.php?id=1100000000964955877 Total factoring time = 4452.6960 seconds Initially a PRP99 before the final output, so no big secret here, because currently running on a 32 bits partition because of a software installation failure. A new computer being turned on today for the first time and doing quite well on the motherboard and graphics card, but for now unable to connect with a monitor because of a connector mismatch. Also two more disks lying on the shelf for possible use, so it bit of excitement around right now. I will be checking the two factors later on, but my guess is that we are closing in a little here. http://factordb.com/index.php?id=1100000000965087791 http://factordb.com/index.php?id=1100000000965089453 Here a quite good factor in the first link, considering the size of the whole number. Continuing, it becomes the same P17 in both, but need to do the shopping first and also that I am on a 32 bits partition for now. At least I know the name for this, namely semiprime and also its intended function or purpose. Again the cup of coffee for this as well, because I am not supposed to be cheating either, because in fact I have a couple such being stored away. Right now experiencing a problem with that of editing, because having two or more different e-mail accounts, each lies in separate tabs and when next using Notepad as well, I am losing track of it despite a possible draft for some of these things, at least when it comes to that of e-mail. If this is because of a recent Windows update, it is not working very well with me and perhaps needs a closer look. The problem is that it is not worth wasting 300 KB of space here only for a given example, so here it becomes only a similar comparison for that of shorter, or "feasible" numbers. Two recent factorizations gave me a composite number when multiplying the two larger factors in each and next flipping around, it becomes a P149 factor. Not reported yet at all, but will be doing so coming up. Only goes or comes to show that perhaps cheating in such a way as mentioned above could also return possible results. The computer being turned on for the first time earlier today could perhaps be able to factorize one number which I think could be a RSA-512 number. Starting with the four digits 9712... from my recall, it could be more difficult than RSA-155, so here a quite good example. But first I will need a Windows installation or setup and for this I will probably go for Windows 10. Now I suddenly found the other tab for this and next it becomes something else. Doing a cut and paste below and will edit it later. Last fiddled with by storflyt32 on 2017-09-01 at 18:11

2017-09-01, 18:11	#52
storflyt32 Feb 2013 111110100₂ Posts	Next at least I know the name for this, namely semiprime and also its intended function or purpose. Again the cup of coffee for this as well, because I am not supposed to be cheating either, because in fact I have a couple such being stored away and again you need to know the intended purpose or meaning, because "" or "x" (small or large caps) is the multiplication symbol and "/" is the division symbol. Next perhaps needs the correct translation, because in my native language, it translates into divisor and dividend, respectively. https://en.wikipedia.org/wiki/Dividend https://en.wikipedia.org/wiki/Division_(mathematics) https://en.wikipedia.org/wiki/Divisor Notice the ambiguation here for the first term, but if I make it 1/7, here 1 should be the possible dividend by means of Mathematics and not any Finance, in the same way as 7 should be the divisor. Suggestions welcome, but will make a fix here. Becomes like that of div and mod for that of integer numbers ("%" when using Yafu) and now my edit disappeared, or vanished. And no need for any draft here since I am lucky to edit my own stuff. The reason for this is the mentioned semiprime or semiprimes and the possible need, or even lack of it becomes to that of possible cheating. If any such, I have never seen a discussion of this and next it should not be about the Scientific Method, or the Method of Proof here either for this. I will do the weekend shopping first, but it could next be split in two parts or halves here as well. I will keep the line above for now, but next did the shopping and are looking for the rest of it. More technically speaking, a RSA number is probably not having any syntax at all. Therefore one set for that of Mersenne prime numbers and also possible factors (2^61-1) and (2^89-1). Is it possible to value a prime number or factor against another when it comes to type, except for being perhaps Mersenne, Fermat, or possibly rep-digit? If I multiply all the Mersenne factors up to a reasonable size (Mersenne23 or less), I could get a decent composite number, but next I do not think that C46 = 1427247692705959880439315947500961989719490561 is such a RSA number either. http://factordb.com/index.php?id=1100000000193090724 This because if so, it has to be specifically designated as such and one reason is the possible bit length of the composite number. Press the More information button here and for the 4246 digit number in the middle, we have a quite good 4182 digit prime. The only reason you sometimes know for that or such for even larger numbers is because you choose to multiply those numbers. http://factordb.com/index.php?id=1100000000964936507 http://factordb.com/index.php?id=1100000000964928845 http://factordb.com/index.php?id=1100000000964928928 Here now three good examples for this, because I added one in the middle and next that these are not easy ones, at least not with 32 bits, running overnight using ecm and still not finished. You are welcome at giving a try, because here no problem with me. Next that this could become a double semiprime of sorts by means of multiplying, or product and could relate to an even bigger number with their respective factors the usual way. Because this is supposed to be about factoring, you also should know in which way it is supposed to be working. A good example is 2 versus 3, or 3 versus 5, because here it becomes either 0.66666...., or 1.66667 if I am not missing something. Next make it an integer number for at least the latter and add a million "6" digits before the final "7". Unable to do it right now, I sometimes am having fun when on a 64 bit partition and next I may possibly get access to another second one in spare. I will be counting my disks later on and will give you a rough number, but for now it became mostly Windows XP here, making for a big problem. Again no point of listing a million digits here, so rather about a given Methodology and this time for that of numbers and not necessarily any science. https://en.wikipedia.org/wiki/Methodology You perhaps know that I perhaps gave mentioning of that of numbers being "poor man's science". In order not to insult anyone, I will perhaps refrain from that, but rather there could still be a possible difference. Getting back at it when I have read the article. Because of the possible limits of factorization, I checked with the msieve application, which for now is a .zip file, but also 64 bits only. I will return back to this when the other computer is up and working. Only that a given C313 or C314 (needs checking) could be having a P156 and a P157 as its possible factors and here we are back to that above. But for now only being aware of the possible limits of factoring and not necessarily "as is" in one given way or another. Checking with the edit for this later on. Last fiddled with by storflyt32 on 2017-09-01 at 23:07*

2017-09-01, 18:55	#53
storflyt32 Feb 2013 2²×5³ Posts	One thing of possible concern, or at least thinking about, is the possible "superhighway" of prime numbers which possibly could be there. Many numbers still remain to be factorized, like that of RSA-1024 and RSA-2048. Either they are at least semiprimes, or possibly RSA numbers, but if together with family of friends, it could end up being 2, 3, 5, 7 and so on and next not much more. The reason why at least RSA-256 is no problem today and RSA-512 could be factored at times, is no excuse for the fact that the number of possible factors in total could be very large. RSA-1024 is not possible to factor directly, so here another example. First of all, this has not been keyed in yet, so please if you could skip this for now, I would be very glad or happy, because this became a sequence and having it keyed in in a proper order, could make for both me and others feeling better. P40 = 1206141817390868369904697458937941898139 P89 = 15316861479442889529311995789441719383377177013171568971730011284995339928476982696581569 Becomes a C128 as the product here and probably possible to factor using msieve. Next try the C128 from RSA-1024 (the Magic Number) and you get the P149 with a little in between. http://factordb.com/index.php?query=%282%5E48853-1%29 My favorite above, except for perhaps the syntax, but should read (2^48853-1). Here the P1764 became my first better find or discovery and working hard here, it mostly sorted out. The remaining C12593 is a "beast" of a number and perhaps not doable at all, even with a new computer soon ready. My current record is not the P1764, however, but rather a PRP12576, which is a gigantic prime and also that there is a 17 digit difference from the C12593 above. I happen to know that the P1764 and PRP12576 are related with each other in one way or another, but which one, or how, I really do not know. Next that I also know that it does not divide the other way either, even when making the C48853 twice, or four times as large in size. You always make it 210 for that of 2 * 3 * 5 * 7, but next "what next" in such a sequence when a possible relationship between numbers is not directly available or present? I definitely know that regular sieving is one possible option or alternative for finding prime numbers, but perhaps not the perfect solution either, because a 321 number or Cullen/Woodall number always needs to be processed by means of LLR. My guess is that the P1764 and next the PRP12576 could theoretically be making the next number in the sequence a possible megaprime, but here I would like to ask for a possible way of getting at such a number. Because the PRP12576 is not readily available or in front of me (I could be checking in with BOINC for this), I do not have it right now. But only that I mentioned the fact earlier on my possible guess or suspicion that it could go straight up for some of the factors in a sequence and next I did not know the way in which to proceed. Last fiddled with by storflyt32 on 2017-10-15 at 14:19

2017-10-15, 05:53	#54
storflyt32 Feb 2013 500₁₀ Posts	Continuing on a Windows, 32 bit partition right now, because of a bit of problems being experienced. Also need ticking the stay logged in box here in order to keep the current session, so now this was done as well. http://factordb.com/index.php?id=1100000001053969348 http://factordb.com/index.php?id=1100000001053969978 P64 = 6521004766994961131998652758478623734567850934300959187999440927 P72 = 132630796754188196686159842513385353980595967923227514053572714567610003 Here both are end factors from two different factorizations, multiplied with each other. Not that unusual perhaps, but here both slightly easier and also slightly better as well. http://factordb.com/index.php?id=1100000001054063735 http://factordb.com/index.php?id=1100000001054062880 The second link above has a pair of P40 and P96 factors and next took some four hours on Windows, 32 bits. Initially a PRP96 here, except for perhaps the dinner in the meantime. The second was started only a couple of minutes before, so here no factors yet. Returning back to the desktop, apparently more easier here, because the word or phrase "either / or", could sometimes be part of Logic, but next also which one should come first, or be better. Also when editing that above, for some reason I had become logged out and therefore made it impossible to post. A little bit of unusual perhaps, but at least now I know when it happens. Here a pair of P26 and P129 factors, respectively and perhaps could be added first when having the early dinner put away. Also that here it took 3 minutes and 30 seconds only. But except for that, the first pair is a pretty good one here and I will have it in a short time. But rather becoming a bit confused that only a C99 makes for a bit of a show, or at least juggling, by walking through the complex process of echoing lines like "Bpoly 3484 of 4096: buffered 538 rels, checked 105253 (8.95 rels/sec)" to the screen in successive or repeating order. Taking a long time as well, here perhaps yet another example of factors which could be sometimes individually known, but when next multiplied, it makes for such complexity. Perhaps not directly stated, but we may eventually find ourselves in a situation where we need to know each small part or step of the whole road, leaving nothing in between, or left. If I ever asked myself what is on the "other side" of that of the Magic number (RSA-1024) and the larger cousin RSA-2048 and next the fact that it does not divide here, but only becomes smaller factors. So here not a good example at all, but also that a P153 was being found earlier today from doing it the opposite way, namely by means of multiplication and next the regular thing. http://mathforum.org/kb/message.jspa?messageID=7890114 Here a quite good example of such factorization which is next some 5 years old, but is perhaps known. Except for that, possibly will need to break off a little in order to not disappoint those in charge of running the projects under BOINC and their respective deadlines. Perhaps needs a bit more editing above, because it became a little bit of butter on bread here. Last fiddled with by storflyt32 on 2017-11-06 at 03:40

2017-10-15, 14:49	#55
storflyt32 Feb 2013 2²×5³ Posts	Here a bit of surprise right now and also a good reason to quit for the day. Ending up with a P260 in my factorizations, checking with RSA-2048 first, which is not making for any good. Next the C1133 of (2^4096+1) which of course is Fermat, but here apparently a PRP871 the other way, with only factors 2^3 and 7 in between. Anyone better here, because I do not recall such a thing myself either. Just in the door, I could perhaps have it later on at a better time and also could be of interest for the larger Fermat numbers as well. Continuing here, but some good news right now. Finding or getting across a P60 today, where the other factor is a P13, the first is a pretty nice one and next trying out with the well-known C147 Aliquot sequence number. http://factordb.com/index.php?id=1100000000633991051 Here getting P1 = 5, both ways in between, for some two factors, the other a P87, but next that I have not reported it yet. Apparently closing in here right now, because the other way around could be even more difficult. http://factordb.com/index.php?id=1100000001061898387 Edit: Together with the Friday beer, giving it a try here as well. Apparently a P25 or so at first and next I will let it go, or continue. Because here or next some other stuff as well, taking up a bit, or if not considerable amount of time and next also I am also proud as well. I will have this one also shortly, except for perhaps not being a better one. Edit: Could add that I lost a P166 right now, because the computer went into a freeze and became unresponsible, needing a restart. Here also a pretty nice looking number as well, so a bit of shame when it happens. It should be the mentioned undervolt problem here and right now my CUDA tasks for the two projects are not running. Next the P50 from the C147 Aliquot sequence number and at first an even number here before next continuing. http://factordb.com/index.php?id=1100000001062276468 Eventually getting it sorted and next having the P50 here. http://factordb.com/index.php?id=1100000001062280638 Also that this could also be work in progress as well, so next also that above for both the P22 and the P68. If next continuing, perhaps something else or different, because this time again flipping around and next for something a bit larger. http://factordb.com/index.php?id=1100000001062282513 Here adding both the P13 and also the P21 when first starting up with C11 = 14807725969 (or 121687 * 121687) . But again that both prime numbers and also factors for such could be telling about a possible weighted distribution of such numbers when looked at or viewed in a larger context, except for sometimes making them more or less equal in size, if not even comparing their individual sizes against each other and also their possible relationship. Giving the above a thought, perhaps. http://factordb.com/index.php?id=1100000001062284241 Here adding a P22 as well and it becomes a loop or cycle of sorts, because I could be back at a previous found factor once again. But next that even a piece of cake does not help right now and therefore needs a bit more of thinking. Next doing so and the P22 apparently is a common divisor among two different numbers, leaving only the P50 and P68 here. http://factordb.com/index.php?id=1100000001062280639 http://factordb.com/index.php?id=1100000001062284242 Therefore the flip around is needed here for possibly anything more and will have it in a short while. http://factordb.com/index.php?id=1100000001062286920 http://factordb.com/index.php?id=1100000001062287002 Again it apparently works out quite well, except for perhaps making a guess for the C117 in the first link above. http://factordb.com/index.php?id=1100000001062288152 Here making perhaps an unneeded entry because I could be still sleeping, so my apologies for that. But rather that the C117 could be multiplied with such a number as RSA-155 and next taking the square root. Here a P20 for this which will be added in a moment, but next should be the same flip around in order for possibly even more. Perhaps time for making a new one here, but before I go for tonight, again being a bit more brave and next adding a P141 to my list. The PXXX of numbers, where at least the first X should start or begin with that of 1 as a digit, is perhaps kind of a motorway, if perhaps not any superhighway either. I mentioned the falling leaf a couple of other places and also the context in which such a thing should belong. The YouTube video being around and next about such a thing as numbers, could be telling about both such a tree for such numbers and also their weighted distribution, if not any relationship as well, as mentioned above. The larger you get for that of the size of such numbers, that of Probability and here Number probability, should perhaps be telling about such a possible distribution. https://en.wikipedia.org/wiki/Probability_distribution Should there be more large prime numbers than those factors which could be small, only because of their size, or is it perhaps vice versa, or the opposite way around? https://en.wikipedia.org/wiki/Mersenne_prime Next reading the footnotes, some four in all, after the List of known Mersenne primes a little down the page. The links above should be in the opposite order, but getting back at this tomorrow. But only that a bit of a gap could be visible between at least M48 and M49 here, except for making no guess or even notice that such a number like P1 = 127 is supposed to be a Genefer factor. Or perhaps I am wrong here? Checking with this tomorrow, because for now it became late night here, but for now at least not in the list of large prime numbers for the latter. Last fiddled with by storflyt32 on 2017-11-06 at 17:45

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