-   storflyt32 (
-   -   Except for the last page, the previous thread became a bit long. (

storflyt32 2017-03-24 01:35

Making a new post right now, because I am still thinking about, or fearing about the following.

Namely: C180 equals or is P90 * P90.

C309 - C180 is a C129 or so.

We already know that story.

"Wind him up", the common phrase being around or heard.

Is it not the fact that this is in fact happening right now?

Gradually it becomes more difficult within a given sequence, or interval of numbers, because of such a thing being a reality.

Perhaps not visible and perhaps not the best explanation either, I mentioned the "method of elimination" and regardless or whether or not a different translation or explanation of such a thing could be possible,
I could be fair right now and only thinking in the context of numbers.

Multiplying a P25 with a P37 could be somewhat difficult and next what about such a composite numbers in regards to or related to something else?

Needs checking.

storflyt32 2017-03-31 15:38

Apparently a fly or insect woke me from my late sleep and perhaps I should say thanks this time.

Need the cup of coffee first, but the clock on the computer is showing wrong, also a reminder about the weekend shopping in a similar way.

More important perhaps, at least two good factorizations yesterday, where one still returned a "failure to equate equation" message.

The number was a C94 and the smallest factor was a P44.

Also a pair of P39 and P40 factors earlier on.

Getting back at the list in Notepad, it becomes a P44 and P51 pair.

This one definitely was a quite difficult number to factorize.

Again, with the cup of coffee in my hand and next have to do the shopping, the right moment is not there right now.

I will get back at it later, together with the links for this.

Right now it became 20 minutes past midnight here, but in fact was thinking about going for my first beer right now.

I came across a P155 a short while ago which could be added later on.

Also not tested this factor yet, but will do so in a short while.

I was thinking about both a factor upload once again from my list of small factors, which was added on.

Also the slightly more important thing of doing the same on the P100 or larger factors still in my list, but which has not been reported.

The problem is that the list both became unsorted and also not completely clean.

I will need to remove both the dashes separating those blocks where the sorting could eventually take place and also a couple of composite numbers should
better have another file for its location.

Also could be added that luck apparently struck late in the last session, which makes me being late in the day.

I happen to know that a number like RSA-2048 could be having both a privacy issue, as well as that of a similar cryptographic such as well.

Because of that I happen to be of the opinion that we could perhaps stick with this issue and keep it this way, if possible.

But also the fact that this number is not too far off now when it comes to its possible factorization and could be so in the near future.

Saying so, because as mentioned, the last session ended up quite well and here another example that this could in fact be accomplished.

More after the first beer or two.

A little more right now. The P155 being found is not the same as a P155 already reported, but slightly larger.

Multiplying the two factors and you get a typical example of a "semimprime".

My guess is that this term perhaps should go for prime numbers instead, but next the question of any practical use of multiplying one of the largest Genefer primes with the largest Mersenne prime
in order for the composite number being returned.

In my opinion keying in a 94 digit number for a secret code because it has only two quite good factors, is a better option in my opinion, but here it became known.

Two people speaking different languages need an interpreter in between in order to understand each other.

The same goes for numbers like RSA-1024 and RSA-2048.

We use the latter as a means of encrypting information being transmitted between a sender and a receiver across the web, or net.

At least we may think it should be so.

This probably has been discussed before, but either RSA labs happen to have each of the factors individually, or the composite number was being chosen because it was found impossible to factorize.

We probably are left with the fact that if you happen to ask a cryptologist about the time of clock, he or she would only come up with or give you an empty face.

Therefore it becomes that of "scrambled" eggs for dinner when you rather wish to see both the codeblocks and the necessary keys being needed for such a purpose, but again the same thing.

At least from a limited knowledge of this, I could perhaps choose to define a given set of numbers as that between 0 and 255 (8 bit numbers) and next have these in 2^n pairs, where n is again a power of 2.

But if perhaps doing so, I could be back at where I once started by doing this, namely thinking that 2^n+1 could be slightly harder to do.

When I originally started with this, such a thing as 2^64+1 or 2^128+1 (or perhaps slightly larger) was relatively new.

Take the factors of these numbers, together with the known Mersenne primes, at least the smaller ones and there could actually still be some work to do.

Here a good example is 2^127-1.

Speaking of this makes a reminder of the attempt being made at bringing all of this together, by means of a composite number which should be familiar.

For now apparently no breakthrough, but also the fact that the asterisks (*) being put or placed next to "almost" matching factors, happened to be removed.

The factors are still in my list, but the whole testing needs to be redone, where needed.

For now it should suffice to say that I came quite close on this, but next do not have it in front of me.

The C147 probably could be broken or found in the near future, but also here we probably are still a bit off as well.

Two P34 factors, together with a P79 apparently makes a close call here, but need to get back here for the product of these three factors.

Should tell that my father passed away some 1 and a half week ago.

Therefore it gets a point of not forgetting that even such a thing as numbers could tell about your place of living, or the intended meaning of such a thing as well.

Such a thing as "Flatland" could have its possible explanation, but not necessarily by means of the tools being used for either computer graphics, or that of computer aided construction (CAD).

Definitely not the same as going in the Church either, because you could be left between a choice between the food you eat and next get rid off, in the same way as that of both birth and death could be that of
cyclic processeses for which no definitive explanations are being known.

chalsall 2017-03-31 22:08

[QUOTE=storflyt32;455904]Apparently a fly or insect woke me from my late sleep and perhaps I should say thanks this time.[/QUOTE]

Just wondering... You're talking to yourself.

I find myself very boring, and I find you much more boring. And you are talking to yourself.

Connect the dots. Answer?

storflyt32 2017-04-01 02:16

Ding, ding...

Edit: Could I perhaps make it "Reply to"?

Edit2: What if I happened to be a scientist and next I possibly could be having an idea?

Oh, we happen to know about that thing, don't we?

Namely that of "In the beginning".

Here at, our main concern or trivial fact occupying our day is that of coming up with a ("possible") prime number which could beat anything else currently known.

The slight culprit, or thing possibly in disfavor is or could be that of "join a project", next be told about given things, or facts, next take these as granted, if possible, but next and most importantly,
the method or methods being used for or in order for a given result or accomplishment in order to be obtained.


Perhaps not the most important here, but the fact that if you happen to be doing any science, including that of possible numbers.

Nasa, as a space organization, chose to both employ and also use the skills of talented scientists in order for a given purpose, namely that of putting a man into space by means of an orbit around the Earth and also that of a
manned mission to the Moon, a total of six successful ones and one ending in failure.

If your talent could perhaps be that of detecting or finding the largest prime number, perhaps not too bad.

But if such a talent could next be put into an even broader perspective, namely that of both understanding that of science, as well as relating that of possible numbers as well, probably even better.

One of the reasons for this blog, if I am not wrong and also even more could be added here as well.


science_man_88 2017-04-01 02:38


there fixed it for you.

storflyt32 2017-04-01 03:11

Thanks, science_man_88 .

For now watching the video.

Watching the light being visible in the video.

Becomes a short commercial break in between.

Possibly two tabs open for this and I have to press the play button in order to continue.

Anyway, no direct reference between that of both light, laser beams, interferometry and that of gravity, which as as possible force, has been previously discussed.

I will check in with the word above.


Despite, regardless, or nevertheless that of, or the force of gravity, or perhaps something else, we should know that this force is not necessarily about any numbers at all, regardless of perhaps being interpreted as such by either Isaac Newton,
or perhaps by Albert Einstein, by means of a given notion of time.

And definitely not that of possible prime numbers either.

Should tell that I give both of these much of my time.

Einstein was dealing much of his "time" with the subject or notion of time, but rather it became that of mathematics for such a thing, including that of both "Field equations" and also that of tensors for this.

If I happened to attend a mathematical lecture or lesson about that of (meaning the subject of) algebra at school, a given notion, or rather a practical explanation about this or such a notion could possibly not be returned or given by means of such algebra.

For some reason, the movie industry chooses to make, or rather popularize, a given subject, which by means of a scientific approach may seem or appear to be either unrealistic, or most likely not possible, namely that of "travel into the future".

Look at such a thing as both algebra and also that of a given understanding of both number factorizations, as well as that of prime numbers itself and it should be evident that such a thing is neither feasible, nor possible.

Heck, if I happened to know that a C200 was the product of two P100 factors, the scientific method, or at least the method being used for such a factorization could tell me this not to be either true, or at least not possible.

So, why are we speaking about such a thing at all?

Really, not the most important thing of all, because I already mentioned Albert Einstein above and the fact that a couple of things could still be "murky" science.

storflyt32 2017-04-01 03:30


A couple of factorization attempts being done or carried out here.

This number is having a P35 or so, meaning factor.

Pressing CTRL-C when running out and next the NFS command on the number, nothing more here.

Needs a complete redo here, which could take an hour or two.

Yes, the NFS command, or its possible implementation in Yafu is definitely better than nothing, but from above not perfect or flawless at all.

Here the developers need to look at a couple of things in my opinon, because here it is not perfect.

Giving a try on the number above using ecm.


Here "failure to equate relation" is being listed nine times in a row before the factors become visible.

Despite being an uneven pair in relative size, this C97 apparently was not the most easy one to factorize.

Also finished the circle here after noticing that there is also a P144 at the other end.


Next I will need to get back at the relationship between these numbers, because there are two other such ones as well, both quite difficult.

storflyt32 2017-04-07 01:30


Perhaps a bit of fun, or possibly that of an irony instead.

At the moment of writing, this number is still a CF.

The C86 remains to be factorized and could be so in not too long.

But the funny thing is that the factors are being found in one of my files, by means of pure numbers only.



The last two factors in the sequence above.

Where did these factors came from, at least the two last or latter ones?

Still needs a redo in order to have it uploaded.

Edit: So where is the "heavy" hand located in all of this?

Should I perhaps make it "heavy hand" instead?

The C67 made it into a pair of P31 and P36 factors.

You probably know that such a thing partly could be processor dependent or dependant and for such a reason I could be sitting on a list of factors which still have to be reported.

What if science perhaps could be fun, including that of dealing with possible numbers?

If I for some reason was able to say that a C300 was a product of two P150 factors, you probably would make a fool of me, because that or such a thing would be impossible.

But next, if you happen to think, or perhaps believe, that a number like RSA-2048 could be having some 617 digits, next a couple of questions could be on your mind.

Oh, if this web-page should still about the possible largest prime number which could be found, such a thing definitely could make a fool of myself, of course.

storflyt32 2017-04-07 07:29

In fact, I hesitate to report a couple of these ones because of the software itself, meaning algorithm.

Meaning perhaps better off, such a thing should perhaps go for that of RSA-1024.

Oh no.

In the world of Seti@home perhaps.


Or perhaps the hit-in your head hammer, meaning that of a possible sledge hammer for such.

Give me or perhaps "it" a try if you will and next why (or how) it don't or doesn't work.

Anyway, should tell that at least some of these broke and is lying aroud here.

Really it depends on the number itself or alone.

Some of these are more difficult to handle or deal with.

One of these, a pair of P35 and P191 factors are a typical example.

I will have it for you later on.



Here are some nice factors, but the FDB only returns P1 = 2 in the second link when keying in.

Anyway, at 08:25 AM in the morning, time to go to bed.

Should tell that with respect to both that of privacy, as well as possibly cryptography, I ended up with two factors this morning, which are having P1 = 2, P1 = 3 and P1 = 5 in between,
both ways for that of a 617 digit number.

I probably will not report this right now, but for now should tell that I recall such a thing in the past and also being mentioned here.

Right now I do not have this number, but as far as I am able to tell, this is probably the closest call or match yet.

Could next test each of the two factors against the C1133 of (2^4096+1) because there definitely is a relationship here which have yet to be found.


Should tell that this one became one of my better ones during the week.

I took the opportunity of comparing with RSA-100 when it comes to this number.

This makes for still one part of it, some 100 digits yet to be reported, but need to look around for this.


This one someone else was able to do when checking in.

Nice and it will add to the whole thing.



Here really only the C89 becomes in question.

Should tell that apparently this one could be a difficult one, because when doing it the opposite way from the magic number you know, it becomes a quite good pair, a P21 and P197.

Also the bad thing that I went out for the weekend shopping just before 6 PM yesterday and found the shop being closed.

Therefore I will have the shoes and jacket on in a short while for a second attempt, but the Saturday shopping is not necessarily fun.

Still some three or four numbers in progress, but these are difficult ones and I will have the fun of reporting what I have when back from the shopping.

With the C100 at the top on my mind, this became most of it right now.

Edit: Noted down the factors of the C89 before getting up and running here.

Not as difficult as originally thought, at least when using ecm on this number.





Also the same P56 end factor here, but here referring to the first link above and not the second.

Came across this before the evening coffee.

The two first ones may not be readily done, but at least giving them a try.

The software is telling about an ETA of some 23.06 hours from the start of it when it comes to the second link.

Down to some 18 hours remaining now.

For the first link above I do not have a similar estimate available.

In comparison, the pair of P30 and P56 factors took 53.6911 seconds to factorize.

Next the sad fact that doing the Saturday shopping and next enjoying the beer apparently took a toll, or beat on me.

I was thinking about doing a couple of things, including that of reporting a couple of numbers, but may have to postpone or delay that for later.

Sorry about that, but so it goes.

Check in with the C100 in a while if you wish.



Apparently a P226 at the other end here, but at least the C74 was being done by the server this time.

Perhaps time making another post right now.

But ever heard about "loopback"?


Example here and next try it out yourself.

Apparently it becomes a loopback here and not any or that difficult at all.

One of my factorizations during the day gave me a composite number in between.

For now I have not been looking at this and I will have to get back up my list for this.

Everyone knows that I am working on this....

I have to stop here.

Back tomorrow.


Anyway, became a bit long perhaps, but here was a quite good one at the end.


Got a bit more than expected here as well.

Apparently a "failure to equate equation" message, but this is a quite good pair.

SIQS elapsed time = 4512.1151 seconds.

Needs to get back to checking for the Magic number directly against or versus this number, because there could be intermediate results, or still a composite number.

But only 09:23 AM in the morning here, so this will have to wait after the evening coffee.


Anyway, it becomes giving a try on the C146.




Became finished after taking some time and as should be noticed, it becomes a loopback here, with the same three factors for all of it.

Right now wondering about how much there is still to go or remaining on this, since I am only left with a poor keyboard and mouse and only a Notepad search function or button for a couple of opened files.


Becomes a P123 being added and I do not know from where.

Needs checking, but a couple of more factors being stored which have yet to be reported.

Also had to write down the numbers and store them here as well.

I will have a cup of coffee before continuing with the rest.

There is a P74 in my factorizations. I will have it for you later on.

Meaning that P27 * P37 * P44 * P74 makes for something I still do not know, but could be able to find, except for also a P54 and a P123 as well.

Next the fact that any prime number possibly in between could be still as hard to find.

Better create a new post.

storflyt32 2017-04-17 17:36

A bit interesting while finishing off the last three beers.

P54 * P74 makes for (2^3) * 5 * P180 when doing it the opposite way.

A P37 different than the P37 above makes for a better factorization of a C147 in pair, so here not too far off.

Also a P60 being added to my list and also a P37 from a C184 (a different one).

But right now it became the end of the day here, so the rest will be for tomorrow.

- - -


ans = 16821990343253548090669268872290873662704331595155716853215743223815573253


SIQS elapsed time = 107131.8256 seconds.

***factors found***

P71 = 86008001756563880037319705217603661451969414306295966789160804218805323
P41 = 19558634080194454480169313467673487022977

ans = 1

Guess what I found.

I have not reported this factorization yet, but this is a very good one, in my opinion.

I think it should be no point reporting it yet, because there is a P27 and a P74 in another window and it could be nice to put the P71 and P74 together for a comparison.

Also could add that the C112 becomes a bit too small for the flip-around in the other end and therefore stumbles or gets lost on a C177 which could be even more difficult.

Rather it could be interesting to compare the individual factors with the larger Fermat factors, at least when it comes to my preference.

Even better would be comparing with any similar factor when it comes to size and next see what could be in between when making the "division" from the larger number.

Make the discovery before the details perhaps, but not getting it looking well.

Returning back at the computer before 8 AM in the morning, it now also has made it through the other way as well.

Becomes a pair of P47 and P131 factors here.

Total factoring time = 28085.3254 seconds, but not any SIQS here, since this is a direct factorization only.

I will have the cup of coffee first.

Becomes a P140 added to my list, but the C146 in progress ran out and nothing more from the NFS command either.

Also to large for SIQS here.

P44 * P47 * P54 makes for a P147 the other way, as well as some small ones.

Could perhaps add a little more here, since there was a post in edit which I canceled after making a copy of the contents.


This one was difficult, by the way.





Here rather the larger factors should be sufficient, but the fact that when "adding" more factors by means of multiplying, like the P14 above, the sequence becomes a different one and needs a new run.

The problem is that if I multiply four P60 - P80 factors with each other, I get a C240 - C320 or something like that.

Or, perhaps make it a bit simpler, doing this with only two factors and next adding or subtracting 2 from the product, it likely will be a composite number.

Multliplying a possible endless sequence, or at least long such factor list and you still end up with a composite number.

If a given method could show me directly (except for sieving) that being able to find a prime number only by such addition or subtraction, that would probably be a nice thing.

But apparently this is not so, so here we are still back at the way we think this should be done, for the lack of anything else.

storflyt32 2017-04-20 19:20

Becomes the cup of coffee right now and next having a couple of beers.


Only a C40 here, but had to add the factors manually.

Also could add that there is a P248 in the other end from the Magic number.

Or should it perhaps be at the other end?

Have not yet checked this factor, because it came in the door with the coffee.

But it will be added to the database at least when continuing with the factor upload.

Again the problem with both the stuck hands and the poor keyboard and mouse here.

Editing above and the P248 should be reported as soon as possible.



Anyway, I should have rather left alone the original text, or be leaving it as it was.

I have not been working on the C617 in detail, but the question becomes how many factors by means of numbers meet with each other, or becomes fully factored each way.

Here it apparently does with a P20 in between and next a PRP336.

I could add this one as well before I take a break.

Also it becomes a loopback at the P248 here, but perhaps not necessary to add.

More interesting perhaps should be the P20 in relation to the C617, since both the P248 and the PRP336 mutually excludes each other from the number in question.



Adding the P10 in the second link, but having the rest of it for both.

I could leave it for now and not doing anything, but using ecm with 2^21 curves here, it needed 4293 curves for the P29 and P36 factors here.

Also it should be a flip around from a larger number which needs checking as well and they do not always have to be that large.

Being a C147 this time, it becomes a P25 and P46 pair here, with 3979 curves needed for the ecm.

Getting back at it if there are not anyone else who does, but for now it became the end of the day.

Except for that, also that the C147 almost factorizes close to midnight with P1 = 2, P2 = 17 and P2 = 29 for two factors.

Apparently all three right now with a P36 and P46 for the C82 and I could be having some fun at looking at these results.

Doing so and the C82 becomes the "join" or perhaps merge between the other two factors, sharing one of them, meaning factors, for each of the other two.

I will have it later on, but apparently someone did it for me and I could leave off with the C135 running in the background.

Anyway, this is not something that I do during the day, but still something that could be looked at.

The factorization of RSA-768 is as you know available by means of a .PDF document for this.

768 is not meant to be divisible from 1024, at least not in a similar way or like that of 512 for the same.

There is a number somewhere down my list which could be an "official" RSA-512 number, but next the fact that I happen to lose track of it.

If a possible comparison between that of RSA-155 and that of RSA-512 (notice the difference) should be made, the latter number could "theoretically" be more difficult,
but here I have no proof.

Only the fact that RSA-155 became factorized and also is the perfect "slingshot" number, except for that of 2^4096+1, as you probably know.

Next what I believe to be RSA-512 still has to become factorized and could be a very difficult one so.

Need looking up the number for this here.

Anyway, if I got the factors for the C82 here, assumedly it would be similar to or like that of the C135 above, I guess.

Remember the fact that both the individual factors for RSA-768 and also the C232 as a whole does not match in or fit with that of the "Magic number".

Of course we rather could be discussing Mersenne 48 or Mersenne 49 instead, but for now I rather do not see the point.

My guess is that before checking, none of the factors in my list do not divide the magic number.

Also there could be one more such available in my list, but I have not been looking at that one.

Perhaps "fake it", or maybe cheating a little and assume or presume the factors of RSA-768 to be "loose" factors.

But apparently not so when it comes to the Magic number and in mathematical terms it becomes "RSA-1024" for this.

From what I am able to tell, this number is the perfect research number for a computer like this one and possibly the " " 's above are not needed.

Perhaps should not be discussed or mentioned, but I happened to give some time regarding that of a possible "RSA-4096", but apparently not able to find an example.

If someone could have been so polite or "cordially" in the past telling me that a prime number could possibly be found by means of 2^n - 1, where n is a P9, or the like,
most likely I would be happy, but apparently not so.

A P12, meaning 2^n -1, where n is a P12, most likely should be composite and next we also should know about that of sieving for such a thing.

The fact is that I happened to be running PrimeGrid and also getting PPS Sieve Jade (10 million sieve or sieving credits) without actually knowing what I was doing.

That is the silly part or point of it and also another part of the story.

Any factors or factor list being returned for now being returned becomes part of the internal structure, or storage system and at least I do not have it.

For now, Prime Sierpinski under PrimeGrid is back at more or less "nominal" values or perhaps numbers when it comes to the tasks in question.

For that of SoB, or Seventeen or Bust, the tasks apparently has become lost or in "haywire", meaning limbo and also I am not running these tasks either.

You probably know that I am not the one doing the "cryptographic" thing either, by means of perhaps guessing a couple of things from what should not be there.

I have yet to add Mersenne 49 to my disc, but next remember the fact that I did so when it comes to Mersenne 48 versus the largest Genefer prime.

For which purpose you may ask and could such a thing perhaps fit your wallet, or perhaps notebook?

You probably know that there should be no point of doing such a thing here, or at all, but what next about the rest of it?

Should it matter at all, or could it rather be more or less wasteful?

For now I will key in the number I got ending with 5 and next continuing from there when it comes to my factorizations.


Here another problem being noticed.

Getting slightly tired, should I return back to the Magic number for the rest or remainder here, or should I perhaps or rather continue in the ordinary or usual fashion?

You know, during the day, the rest, or remainder of it, could be in another window, but in the late night, together with a beer, I get stuck in the mud.

For now it becomes a C139 when returning back to the Magic number and here it will no more.

My guess, or presumably the same will be when it comes to the FDB as well here.

Perhaps this is the reason why I am having a list of P100 + factors, but not any similar for that of any P50 - P100 factors.

Again there is no point for me, or anyone else for that matter, of multiplying two P90 factors and next think you have the rest.

Oh no and so it goes, or should have been for a long time.

Anyway, or oops, the square root function or the "straight number" may of course not be used here.

Next. I forget the correct or proper word being used here.

Getting back at it.

If we rather could look at smaller RSA numbers, it probably could be shown that there is a given method for it.

But next which one, or why.

Again, reminds me about the feather for such a thing, but right now lost the word.

Also the problem that the text, or contents, could still end up being a bit long and when chioosing to edit, the contents could become lost, making for yet another copy and paste into Notepad.

Not a good thing, but except for that, if I get a C135 for which I do not know the factors for, what is in the other end?

Always needs or becomes checking and most likely it becomes a composite number.

Here is perhaps one of the main points.

A P112 "divides" or rather factorizes from the Magic number into a composite number which is having no small factors.

Then, or next. it becomes yet another sequence, with a given number (like RSA-155) in between and guess I am not silly.

Still, this becomes a fact and for this a possible workaround by a given method, resulting in yet another factor most often, or most of the time.

Another edit, or perhaps posting.

I had the Thursday beer. My apologies.





Here is a bad example for you.

By the way, I lost the C135 in progress overnight and needs a redo.

Need checking with the links before finished, but here is an example where it apparently does not work.

Only remembering that I gave the C186 a couple of hours a while back, without success.

Adding the P41 and PRP (or P99) factors for a C139 a little while ago, we have one side or endpoint for at least one more such pair, but still many more left.

A P138 in one of my windows for the factorizations probably does not make it with the Magic number this time either and this could go on forever.

Definitely this is the main point when it comes to this, but the question is how or in which way you get to such a number first and next being able to know that it is of such complexity.

For most of these numbers, starting the factorization the opposite way only makes it a composite number, like the C186, so the trick here is that of breaking it up in some way, making it easier.

The trick, as you probably know is that of taking RSA-155 for this, multiplying with the composite number and next the square root, because I found it to be an excellent example or choice.

The fact is that it could be difficult or impossible to determine if such a number and also that of RSA-768 happened to be "loose" factors from the start and next could be made such a slingshot at times.

Apparently bit length is a factor to consider as well and therefore the reason that the latter factor or number above did not find any much use for the other numbers being worked on.

I could add the link for the C139 next.




Here the problem is where you should be going next.

It should be quite obvious that pressing the "More information" button should be done, but next which numbers relate to each other.

Here the third link is from the first link and not the second, which becomes another number the opposite way.

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