Pseudo-mathematical gibberings (volume 9a)
 

Sorry!

Really I should have stuck with the -1 rather than +1 here.

But honestly, +1 probably is the hot subject right now. In the end it is more difficult to be working on and have more unknowns than knowns coming along with it when it comes to possible existing factors.

I am using * for multiplication. Some people prefer the . instead.

Anyway, if I try dividing 2^1968721+1 with 31840750786281 (3*10613583595427), I am left with a number which now has become slightly smaller. Unless proven otherwise, it is assumed to be a composite number where still further numbers (prime numbers getting progressively larger and larger) are thought to be part of this number.

Sieving or factoring is supposed to possibly be able to extract one or more such prime number (or factor) from this larger number. Eventually, the factors remaining (if more than one) becomes so large that it becomes almost impossible to get to them.

In comparison, 2^1048576+1 is thought to be a composite number where no factors apparently are known.

If a factor (possibly a larger one), may exist for someone to find, it may possibly be easier to deduce a composite number before a prime number when trying to divide (or factorize) these numbers with each other, like 50/10 rather than 50/5.

Anyway, sieving is supposed to yield the smaller factors rather than the big ones.

FactorDB is your friend
 

Most of your conclusions are right. However, did you try to visualize the number you are interested in. Look here: [URL]http://factordb.com/index.php?showid=1100000000634633435[/URL] . It is a hard nut to crack. It might take some time to see such numbers fully factored (there are some lucky finds in this range, but generally it is very hard). In the future you may want to consult FactorDB before posting a number here. FactorDB might help you define your problem and show you what is known beforehand.

I do not understand why +1 is hotter than -1, but I guess there is an explanation.

[QUOTE=bloodIce;359914]I do not understand why +1 is hotter than -1, but I guess there is an explanation.[/QUOTE]

We love them both equally, but appreciate the former's positive attitude.

-1, OTOH is what in German is referred to as a [i]Sorgenkind[/i].

[QUOTE=ewmayer;359944]We love them both equally, but appreciate the former's positive attitude.

-1, OTOH is what the in German is referred to as a [I]Sorgenkind[/I].[/QUOTE]
Which body parts are you talking about? :shock:

[QUOTE=LaurV;359954]Which body parts are you talking about? :shock:[/QUOTE]
It means: On Top Of Head.

Well, plus one, minus one, I thought he was talking about bra sizes, but giving the positive attitude, it could also mean condoms...

[COLOR=White](what a dirty mind I have)[/COLOR]

Since I have been quoted
 

I hope those friendly comments are not addressed to me. I still cannot get why 2^n+1 can be cooler than 2^n-1. You would ask why I am so negative, when I say that I prefer "-1" :smile:.

Apparently someone was able to conclude that 2^1968721-1 is a composite number as well.

Yes, but anyway, what are the numbers here?

My best guess is that there are no small factors in this number.

Also I am trying out the command
ecm((10344^1024+1)/3243597063038977), using yafu-x64 .

Yes, a new factor apparently having been added there.

Or, alternatively "ecm((10344^1024+1)/3243597063038977)" from the DOS command line in Windows.

3243597063038977=12289*263943124993, by the way.

Apparently, using both the abovementioned command, or the alternative
"ecm((10344^1024+1)/3243597063038977,30)" syntax, based on Yafu, it still apparently crashes out now, both when running directly from Yafu through Windows, or starting up a DOS prompt and fortunately ending up back there. By the way, I only have 8 GB of RAM installed, not 16 GB.

Apparently there is some DOSKEY or the like installed and running, which happens to remember my previous command lines using the up and down arrows on the numerical keypad (NUMLOCK is turned off, by the way).

Should I just push the button for the Microsoft Error Report when it comes to this error problem? The numbers being worked on here are not the biggest ones, but definitely this becomes harder and harder to get at as the smaller factors are being eliminated from the rest of the number(s).

A little edit: Apparently it now takes it, late in the night, in a DOS command prompt window.

Thanks!

[QUOTE=bloodIce;360030]I hope those friendly comments are not addressed to me. I still cannot get why 2^n+1 can be cooler than 2^n-1. You would ask why I am so negative, when I say that I prefer "-1" :smile:.[/QUOTE]
[QUOTE="THIS ISLAND EARTH (1954)"][URL="http://public.wsu.edu/~delahoyd/sf/this.i.e.html"]He meets through Ruth a Dr. Steve Carlson and a cat named Neutron.
Ruth says, "We call him that [B]because he's so positive[/B]."[/URL][/QUOTE]
[COLOR="Wheat"]. [/COLOR]

To be slightly serious, I prefer -1 too; because the techniques that prove numbers prime by computing in a multiplicative group don't have scope for handling (2^n+1)/{something small}, and for nearly all n there is an algebraic something-small.

For example, it took quite a lot of work to prove the primality of (2^42737+1)/3 ; (2^83339+1)/3 looks as if it's within the range of possibility for fastECPP using effort comparable to a 175-digit GNFS factorisation.

[QUOTE=Batalov;360052]
Originally Posted by [B]THIS ISLAND EARTH (1954)[/B]
[I][URL="http://public.wsu.edu/%7Edelahoyd/sf/this.i.e.html"]He meets through Ruth a Dr. Steve Carlson and a cat named Neutron.
Ruth says, "We call him that [B]because he's so positive[/B]."[/URL][/I]
[/QUOTE]

[URL]http://youtu.be/HaK1DPStRUE?t=33s[/URL]

[QUOTE=Batalov;360052][QUOTE="THIS ISLAND EARTH (1954)"][URL="http://public.wsu.edu/~delahoyd/sf/this.i.e.html"]He meets through Ruth a Dr. Steve Carlson and a cat named Neutron.
Ruth says, "We call him that [B]because he's so positive[/B]."[/URL][/QUOTE][/QUOTE]

My favorite line from the movie - still can't believe the MST3K crew missed a juicy razz-fest on that one, along the lines of "OK, at this point I'm not yet sure what the sekrit project of the white-haired big-foreheaded aliens is all about, but whatever it is, it's DOOMED, I tellya".

Although there is another possible interpretation for the cat-called-Neutron comment, other than the "our pointy-brassiered science babe here hath flunked out of particle physics" one. Cue Madeleine Kahn in [i]History of the World, Part 1[/i]:

[I]"We call him that because he has just been snipped!"[/I]

[QUOTE=bloodIce;360030]I hope those friendly comments are not addressed to me. I still cannot get why 2^n+1 can be cooler than 2^n-1. You would ask why I am so negative, when I say that I prefer "-1" :smile:.[/QUOTE]
Stay calm man, nobody is picking on you. Contrarily, all people here disagree with OP's gibberish, they took your remark as an irony and just weighting more into it. As "mersenne hunters" we are all more interested in the -1 side (but don't tell that to my wife :smile:)


By the way, the number in cause is proven composite, one core of PFGW can show it in less than 3 hours.
[code]
(2^1968721+1)/(3*10613583595427) is composite: RES64: [CD2A6ED1468CEDF0] (7234.4788s+27.8081s)
[/code]

Indeed I put some irony on purpose in some of my comments, but my primary intention was to reduce the spam with a redirect to FactorDB. To me it seems that the guy is with a positive attitude (this time no pun intended), but I think his age is well bellow the average of this forum. She/he needs a reference for his quests.

For orders sake.

Being able to determine, or prove, that a 105 digit number is a prime number is an easy task to carry out.

Multiplying two such (different) numbers and then assume that this now composite number is, or possibly represents an almost unbreakable
number when it comes to its factorization becomes an almost impossible or incomprehensible task to complete or finish, even when using a
powerful personal computer for such a given purpose.

Why is this being so?

Because the factors becomes almost identical when it comes to size.

Both these elements are making some numbers
completely impossible to factor, even though some people may be so lucky as to know the individual factors which are representing these
numbers.

Two classic examples should be mentioned when it comes to this, namely RSA-1024 and RSA-2048.

Both these two composite numbers have yet to be factored.

And still, we happen to be so lucky that we "know" the factors which are representing RSA-768.

Please try factoring this number for me. You will be able to find out that factoring a RSA-512 or similar number is an almost impoossible thing to
carry out or do, using a regularly available software platform for just such a use.

One such example for you right here. Give it a try, will you?

7529315904594771817511864427258894764407713405160355555243610
8811740640162856360514781181695040844760480712732512854358557
6730146689356339498615917

Or, on only just one line, for copying simplicity and use -

752931590459477181751186442725889476440771340516035555524361088117406401628563605147811816950408447604807127325128543585576730146689356339498615917

[URL]http://factordb.com/index.php?query=752931590459477181751186442725889476440771340516035555524361088117406401628563605147811816950408447604807127325128543585576730146689356339498615917[/URL]

This number is not an "official" RSA-512 number, but at least it ends up close to it being such a number.

Here is where it is currently standing.

[QUOTE=storflyt32;383740]Please try factoring this number for me. [/QUOTE]
Why? You can do it yourself and fairly easily.

[QUOTE=storflyt32;383740]
You will be able to find out that factoring a RSA-512 or similar number is an almost impoossible thing to
carry out or do, using a regularly available software platform for just such a use.[/QUOTE]
Bull:poop:

@storflyt: please use [code] tags when post those long lines, otherwise the posts are very difficult to read, and people may just close the thread without reading it. Non everybody has wide monitors.

The C147 composite you link in the factorDB is a factor of [URL="http://factordb.com/index.php?id=1100000000633991049"]this C161[/URL], which is one year old, and seems it comes from an aliquot sequence, according with its structure, but I don't have such sequence in my data base and I could not find another reference to it in the factorDB. It may be an "over a million" starter aliquot sequence.

Being one year old (if not fake, and some key for some gaming site, as happened in the past :smile:), it got some ecm done already.

You can factor it with yafu in 4 cores in few days (mostly a week), with [U]an average computer[/U]. There is nothing "impossible" about it, as Batalov already said. I can factor it for you in 2-3 days, if you tell me where the number is coming from, and convince me that it is important to factor it.

If you did not know this already.

If I try multiplying a prime number (or a composite number for that matter) with something else, I am never supposed to be finding any prime numbers this way.

For some reason the process of factorization (meaning factorizing numbers) is not always that straightforward.

Certainly you happen to know that all those numbers eventually are there, but in which way am I then able to get to these numbers?

As usual, every number has its easy part and its more difficult part. It becomes part of a track, similar to the traversal of a tree-like structure (almost hierarchical in nature and shape).

Factorizing a number like 10^4032-1 gives me possible Mersenne-like factor numbers (or what?). Also I am getting what appears to be so-called rep-digit factors. When it comes to the process of finding large Fermat primes, you assume that a number having a notation like xxxx00000000000.....1 is or the similar is prime.

For now, such a number is not assumed to be a rep-digit number, whether or not it is prime.

So at which point does it converge? Please have a look back to my previous analogy regarding 5*7 = 35 and vice versa.

The 5-part is supposed to be the easy one. The 7-part is the more difficult part of the task.

For large numbers like 2^48853-1 you of course are getting something else back when it comes to the numbers, but the way or method (analogy) of thinking is still the same, no matter else.

So, since I have been here for a while now, there is a couple of questions that I would want to ask you.

The subject of prime number finding (or call it factor finding if you wish) is the area or realm or subject field of the
mathematicians. In order to properly be able to carry out such a task, you more or less depend on the processing power of the computer, regardless of how sharp minded you may be yourself.

It really may become too big numbers at times, even for the sharpest of minds.

Not all prime numbers, even the smaller ones, are known today. Some of these may be found by means of factorization.

Other factors are being found on their own, not being directly related to other, possibly larger numbers.

Some people may think of the order of factors as being directional, only being sorted from smaller to larger in size (or perhaps the opposite way).

In other instances or cases, factors or numbers are being related to each other by means of either factorization, or possibly by means of trial division.

At times one may be starting thinking about the individual factors possibly being represented by means of a hierarchical tree structure.

For every branch of this tree, possibly with a left one as well as a right one, or the similar, one branch of the tree may be regarded as more simple when it comes to factorization.

The other branch of the tree then becomes more complex.

Some factorizations are simple, because extracting a factor like 3 from even a 10,000 digit number is a quite simple thing.

In other cases, factorization becomes more difficult, because the factors of a composite number may eventually show up to be more similar or comparable in size.

Examples of such factorizations include the RSA-numbers and the semiprime numbers, including the Mersenne semiprimes.

One may get the impression that at times these numbers may only be found by means of trial division and not by means of factorization, because the processing time at doing such a thing becomes very high. This is the reason why such numbers like RSA-1024 and RSA-2048 have yet to be factorized properly.

Assumedly the individual factors of these numbers may be known to a very few people, but that is because these factors were found individually and not as a result of factorization.

Even more complex, it may seem to, is the factorization of 2^(2^n)+1, where n>= 4096.

Here, apparently no progress is being made despite several attempts.

Is it correct to assume that these remaing composite numbers in fact are semiprime numbers and if so being Fermat factors rather than the corresponding Mersenne factors?

There may be some reason to speculate whether a couple of numbers currently being discussed may be part of one or more of these factors, but for now the question apparently remains open. It becomes a question about computing or processing power and how much time a specific factorization attempt should be given.

At times, no results are being obtained because of the time it may take to be doing so and other events which may take place in the meantime, like system hangs and possible restarts and the like.

First of all, instead of posting in one-sentence paragraphs, which makes it very difficult to read and understand, break your post up into paragraphs of more than one sentence, starting a new paragraph whenever the underlying subject changes.

You asked
[QUOTE]
Is it correct to assume that these remaing composite numbers in fact are semiprime numbers and if so being Fermat factors rather than the corresponding Mersenne factors?
[/QUOTE]
My answer to that is "No."

Merry Christmas!

Thanks for the reply.

Leaving it with one question only today.

What is the point of factorizing a given number when the prime factors may already be known individually?

Apparently the nextprime command built into Yafu is not that error free and it definitely fails when the number becomes large.

Yes, I know that you may be able to find the "previous", or lower factor as well when using this command.

Just by pure coincidence, or what else might this be?

I used the last part of a big number that became lost when it comes to its actual syntax.

The initial number being used I do not have either, right now. I will get back at it.

Apparently some small numbers being factors at the start of the factorization of this number.

From this last part came a P143 by means of factorization. Probably a C160 or larger just before that.

I next divided this P143 from RSA-1024 and of course it did not so.

The result became a C149 which apparently is a hard one to factorize.

Does that imply that I am close to a prime factor (not necessarily that of RSA-1024) when such a thing happens, or is there rather another explanation to this instead?

If you did not know this already, it is really not that difficult finding the next (or previous) prime factor from a composite number if it is not too large. The question becomes what is most needed since at times factorization may be a hard thing to do and the alternative to a brute force attack on a given, composite number, may be just that - a lot of other factors, of which not everyone is that necessary to be having.

Please have a look at 2^129000-1 and 2^1290000-1 in the Factor Database and you certainly will agree with me.

What are you smokin', son?

[QUOTE=Batalov;390934]What are you smokin', son?[/QUOTE]

I'm assuming Christmas stress has brought on this recent bout.

[QUOTE=flagrantflowers;390936]I'm assuming Christmas stress has brought on this recent bout.[/QUOTE]
No doubt some socks were received at Christmas. One can put them on one's hands.

[QUOTE=Batalov;390934]What are you smokin', son?[/QUOTE]

lol

[QUOTE=flagrantflowers;390936]I'm assuming Christmas stress has brought on this recent bout.[/QUOTE]
What Christmas?
[SPOILER]Russian Christmas is on the 7th of January. For those who celebrate it.[/SPOILER]

C97 = 1569682147091252660426459011903371876173700815531481264645611001275182005048286500549521053784939

Try this one for Christmas.

It is apparently a quite hard number to factorize.

[QUOTE=storflyt32;391213]C97 = 1569682147091252660426459011903371876173700815531481264645611001275182005048286500549521053784939

Try this one for Christmas.

It is apparently a quite hard ...[/QUOTE]
/yawn/
You need your apparentometer serviced immediately. It is faulty.

This number takes 2 minutes to factor.
124917870785681646466531593289689829582453 * 12565713273998366817214149865851175556557748151050976863

[QUOTE=Batalov;391214]/yawn/
You need your apparentometer serviced immediately. It is faulty.

This number takes 2 minutes to factor.
124917870785681646466531593289689829582453 * 12565713273998366817214149865851175556557748151050976863[/QUOTE]Hey, can I post numbers here and have them factored also?

Yay, a free factoring service right here on this board.

Thanks for doing that, Batalov!

Much appreciated.

[QUOTE=retina;391215]Hey, can I post numbers here and have them factored also?
[/QUOTE]
Sure you can.
"Why not do a good deed when it costs you nothing", replied the field mouse to Thumbelina. (at least in the Russian translation, which I remembered since childhood; cannot find it in the H.C.Andersen's original)

[QUOTE=Batalov;391218]Sure you can.[/QUOTE]Okay, let's start with MMMMM2 and then move on to RSA4096. Just one factor from each will be enough. Although I am not sure about the ordering in terms of hardness so doing them in the opposite order will be fine also.

[QUOTE=retina;391220]Okay, let's start with MMMMM2 and then move on to RSA4096. Just one factor from each will be enough. Although I am not sure about the ordering in terms of hardness so doing them in the opposite order will be fine also.[/QUOTE]So, are we there yet? It's been two minutes.

Ah yes, but what part of "when it costs you nothing" was unclear? ;-)

I am in a generous mood, and I step up from "nothing" to 2 cents. Here they are - :two cents:

[QUOTE=Batalov;391222]Ah yes, but what part of "when it costs you nothing" was unclear? ;-)

I am in a generous mood, and I step up from "nothing" to 2 cents. Here they are - :two cents:[/QUOTE]Okay, so you are saying it will cost me 2 cents. Then it is a deal. Factors first, then I'll pay.

No, you will get something for nothing if it costs me nothing. It could be much more valuable to you, though. That's what the H.C.Anderson's field mouse told me when I was a little child and I pondered for a while and decided, "you are right, little furry dude, this makes sense".

But because I am still in a generous mood, of course I will help you factor those little trifles!

MMMMM2 (rather properly written MMMMMII, because as you know you are mixing Roman and arabic digits, but that's an easy mistake to make) = 2 · 41 · 61.
RSA4096 is even easier and is equal to 2 · 2 · 2 · 2 · 2 · 2 · 2 · 2 · 2 · 2 · 2 · 2 South African rands.

[QUOTE=Batalov;391224]But because I am still in a generous mood, of course I will help you factor those little trifles!

MMMMM2 (rather properly written MMMMMII, because as you know you are mixing Roman and arabic digits, but that's an easy mistake to make) = 2 · 41 · 61.
RSA4096 is even easier and is equal to 2 · 2 · 2 · 2 · 2 · 2 · 2 · 2 · 2 · 2 · 2 · 2 South African rands.[/QUOTE]Well that is absolutely precisely exactly[color=grey][size=1][sup]1[/sup][/size][/color] what I wanted. So as promised here is my payment.

:two cents:

[color=grey][size=1][sup]1[/sup]Not![/size][/color]

C75 = 480803331333445101741328545933891153031908054791180635359833574231002718203

Same problem here as well.

Edit: Found a PRP614 just two minutes ago. Will be reporting it shortly.

BTW: What is the "official" RSA-4096 number?

Thanks for any answer!

[QUOTE=storflyt32;391229]C75 = 480803331333445101741328545933891153031908054791180635359833574231002718203
Thanks for any answer![/QUOTE]
Just because we can doesn't mean we will.

[QUOTE=storflyt32;391229]C75 = 480803331333445101741328545933891153031908054791180635359833574231002718203

Same problem here as well.

Edit: Found a PRP614 just two minutes ago. Will be reporting it shortly.

BTW: What is the "official" RSA-4096 number?

Thanks for any answer![/QUOTE]

Like Paul said, only the first request is usually free, or else there will be no end to it. You need [URL="http://en.wikipedia.org/wiki/Fifteen_Million_Merits"]fifteen merits for a solution[/URL] of this problem.

Like someone else said, [I]Give a man a fish, and you have fed him for today.Teach a man to fish, and he will sit in the boat and drink beer all day. [/I]

[QUOTE=Batalov;391246]Like Paul said, only the first request is usually free, or else there will be no end to it. You need [URL="http://en.wikipedia.org/wiki/Fifteen_Million_Merits"]fifteen merits for a solution[/URL] of this problem.

Like someone else said, [I]Give a man a fish, and you have fed him for today.Teach a man to fish, and he will sit in the boat and drink beer all day. [/I][/QUOTE]I prefer: light a man a fire and you warm him for a day. Set a man on fire and you warm him for the rest of his life.

C80 = 47696710294705499280359610260517275637267727477058055991019082347840906420354827

This C80 is a stubborn one and right now I do not have the factors for it.

You are welcome to give it a try.

Thanks!

How are you trying to factor these numbers? Pocket calculator?

Thank you for doing that.

Oh, it became a quite smooth pair. What else?

Got a little saturated system before finishing off yesterday and will continue now.

It also became a couple of results which I will update as time goes by.

Hehe, I am almost convinced about the previous discussion regarding the biological or electronic source of the postings. I'm not gonna say the B word because I don't want to trigger an automated denial of some sort in case the suspicion is correct. Any biological reader should be able to easily figure out what I mean.

So If I say - factors - and add a few other terms like - this number with 120 digits - etc. I wonder what will be the response?

Should perhaps tell that I just found a PRP848 here.

I will be adding this factor a little later.

[QUOTE=retina;392329]Hehe, I am almost convinced about the previous discussion regarding the biological or electronic source of the postings. I'm not gonna say the B word because I don't want to trigger an automated denial of some sort in case the suspicion is correct. Any biological reader should be able to easily figure out what I mean.

So If I say - factors - and add a few other terms like - this number with 120 digits - etc. I wonder what will be the response?[/QUOTE]

[QUOTE=storflyt32;392333]Should perhaps tell that I just found a PRP848 here.

I will be adding this factor a little later.[/QUOTE]

This response seems to militate against your suspicion.

Personally, as I've remarked before, I find it much more interesting and unlikely that the user is a b*t. It would have to be a quite sophisticated one, or else one custom-made to discuss mersenneforum topics. Both seem far less likely than a mathematically unsophisticated poster with a poor grasp of the English language.

story: I factored your C80.

[QUOTE=CRGreathouse;392368]Personally, as I've remarked before, I find it much more interesting and unlikely that the user is a b*t. It would have to be a quite sophisticated one, or else one custom-made to discuss mersenneforum topics. Both seem far less likely than a mathematically unsophisticated poster with a poor grasp of the English language.[/QUOTE]
My money goes onto a b*t whose human operator (whether that's the programmer or not) sometimes, but not always,
"helps it along".

Deleted

[QUOTE=storflyt32;392312]C80 = 47696710294705499280359610260517275637267727477058055991019082347840906420354827

This C80 is a stubborn one and right now I do not have the factors for it.[/QUOTE]

Although it would be quicker to install YAFU, even [URL="http://www.alpertron.com.ar/ECM.HTM"]Alpertron [/URL]will factor this, and any other number up to C90.

Yes, but it needs Java (and not Yafu) in order to work.

[url]http://www.alpertron.com.ar/ECM.HTM[/url]

Try it out without having Java installed by using the calculator at the bottom of this page.

Based on earlier experiences, including a massive crash involving three hard discs, I am now reluctant to download and try everything.

So it goes for now.

[QUOTE=Brian-E;392380]My money goes onto a b*t whose human operator (whether that's the programmer or not) sometimes, but not always,
"helps it along".[/QUOTE]

That seems almost non-falsifiable -- anything sensible the user says can be attributed to human intervention.

[QUOTE=CRGreathouse;392743]That seems almost non-falsifiable -- anything sensible the user says can be attributed to human intervention.[/QUOTE]
Yes, indeed. It's a pity that reality doesn't always take care to be provable or falsifiable.:smile:

Question for you.

If you do not mind.

[url]http://factordb.com/index.php?id=1100000000621571620[/url]

This number is the product of the P252 factor of 2^1024+1 and the the P564 factor of 2^2048+1.

I can update with the factors if there are no objections to this.

Nice done. Thanks!

[QUOTE=storflyt32;393369]Question for you.

If you do not mind.

[url]http://factordb.com/index.php?id=1100000000621571620[/url]

This number is the product of the P252 factor of 2^1024+1 and the the P564 factor of 2^2048+1.

I can update with the factors if there are no objections to this.[/QUOTE]

This is not a post from a bot. It is the post from an asshole who posts just to be annoying.

I will answer the question. The answer is:

One of its legs is both the same.

Lkooing to the "more info" tree on the fdb, tohse two are konwn from 2013, but tehy were used recnetly to gerenate ohter bgiger cmopsoite nubmers with over three hnurded dgiits by repetealdy mulplitying them with tewtnysveen dgiits pirmes, lsat one two dyas ago. So, it smees he is aslo fldooing the db with siht... It may be tmie for a new logner :ban:

:smile:

[url]http://factordb.com/index.php?id=1100000000744870056[/url]

How did this one come up?

Was it perhaps the result of two different factorizarions?

Oh, yes!

Thanks for calling me an asshole, Mr. Silverman.

Maybe it shows up in the food I am eating.

Numbers are not supposed to be hiding any secrets alone. They are either prime or composite.

If they happen to be composite, it is because they happen to be the product of two or more factors which are supposed to
be prime.

The amount of different numbers are supposed to be almost without limit. Consider infinity in this case which becomes a
number that has no meaningful definition.

The more numbers you start factorizing, the more factors it becomes.

RSA-768 is such a number.

It became factored but it could well have been left unfinished and been used in a certificate instead. For a single computer this number definitely stands its position, at least when comparing with slightly smaller number that are almost as difficult and not being factored yet.

Am I supposed to be doing this just for fun, or is it still something that I am possible able to learn by doing this?

Consider a textbook.

The author is giving examples. At the end in each lecture he or she leaves an example for the reader as an exercise.

Which is showing that there is always something around that you do not know about which has to be tried out.

I only have a few precious brain cells left, please somebody stop him before he kills the rest.

:ban::ban::ban::ban:

[QUOTE=storflyt32;393465]

Numbers are not supposed to be hiding any secrets alone. They are either prime or composite.
[/QUOTE]

If by "number" you mean positive integers then 1 is neither -- it is a unit :smile:

This question for you.

You certainly already know that I do not bother too much about codes and secrets, but rather am having an interest in numbers only.

I happened to stumble across a quite good factor here a little while ago.

The Yafu factorization software as you well know does not divide two numbers correctly at all times.

Like trying to divide 7 with 3, I get 2 as the answer.

For an even bigger number the returned answer may be something else in between.

The result I get becomes an approximation instead if such is the case.

But I next tried dividing this number from the C617 which is representing RSA-2048.

The number I got was an even one which therefore was divided by 2. Just using ecm instead should go for the same.

The interesting thing is that the number I get next is also a prime factor.

The two factors are quite a bit different when it comes to their individual sizes.

Because this did not end up being the correct factors, I may very well be in for a new complete cycle again.

Or did I perhaps stumble across something this time?

Apparently multiplying the two factors alone did not help very much here.

You stumbled with your left foot across your right foot, man.
This (masochistic self-humiliation of yours) has got to stop.

Your postings make people's eyes and brains bleed.
Every time they come in this thread (if they haven't yet learned their lesson to simply never visit it), they want a minute of their life back.
But they can't. There is no refund.

[COLOR=DarkRed]Let's start with 24 hours for you to think. Next time it will be a week.[/COLOR]
:moderator kitteh:

[QUOTE=storflyt32;393465]Oh, yes!

Thanks for calling me an asshole, Mr. Silverman.

Maybe it shows up in the food I am eating.
[/QUOTE]

It shows up in the repeated gibberish that you post.

If you don't like being called an asshole then stop acting like one. Stop
posting spam/gibberish/word salad/complete nonsense.

Your posts are entirely devoid of any meaningful content.

[QUOTE=R.D. Silverman;393668]IYour posts are entirely devoid of any meaningful content.[/QUOTE]They are, however, confined to the padded cell of Miscellaneous Math[SUP]*[/SUP] .

If you can't stand the inmates, get out of the asylum and leave it for those who can tolerate gibbering idiots.


* Assuming the mods are doing their job.

[url]http://factordb.com/index.php?id=1100000000747119026[/url]

This one I came across tonight.

The dinner took a little time to finish off, so I let it run.

When continuing the session, I noticed this quite large PRP794 factor.


[url]http://factordb.com/index.php?id=1100000000747133559[/url]

Also this one late tonight with a late cup of coffee and a dessert.

(2^274177+1) / 3

Composite.

Here is [URL="http://www.primenumbers.net/prptop/searchform.php?form=%282^p%2B1%29%2F3&action=Search"]a list of PRPs of this form[/URL]. The last on the list has been [I][URL="http://primes.utm.edu/primes/page.php?id=118512"]proved prime[/URL][/I] by Tom Wu.

Please tell us when you have a PRP over 10 million bits -- comments such as "is composite" are silly. :loco:

Thanks for the PRP list.

Since (2^65537+1) has factors 3 and P14 = 13091975735977, but not the (2^114689+1) / 3 in between,
the latter number is also composite.


(2^114689+1) / 3

Composite.


Sorry about that.

But I am really of the opinion that you do find more "factors" by means of factorizing than just doing a PRP test on a larger number which most likely is composite and also takes much more time to compute.

Oh, I guess you really don't like me very much.

Tested out the following using WinPFGW (64-bits version):

winpfgw>pfgw64 -q"((10^35041*4-1)/378842763)"
PFGW Version 3.7.7.64BIT.20130722.Win_Dev [GWNUM 27.11]

((10^35041*4-1)/378842763) is composite: RES64: [7F1166706CE487EA] (103.7602s+0.1324s)

Therefore, (10^35041*4-1) should be composite as well of course. There were some factors there a little earlier on, but now they are gone. Possibly I am doing this wrong. I will get back to this a little later instead.

[QUOTE=storflyt32;395734]Oh, I guess you really don't like me very much.

Tested out the following using WinPFGW (64-bits version):

winpfgw>pfgw64 -q"((10^35041*4-1)/378842763)"
PFGW Version 3.7.7.64BIT.20130722.Win_Dev [GWNUM 27.11]

((10^35041*4-1)/378842763) is composite: RES64: [7F1166706CE487EA] (103.7602s+0.1324s)

Therefore, (10^35041*4-1) should be composite as well of course. There were some factors there a little earlier on, but now they are gone. Possibly I am doing this wrong. I will get back to this a little later instead.[/QUOTE]

What compels you to keep posting clueless drivel?

I do not know you personally, so I neither like nor dislike you.

I am, however, totally contemptuous of your posts.

Factordb number.
 

[url]http://factordb.com/index.php?id=1100000000760181579[/url]

This number was found by means of factorization.

I did not have the individual numbers in advance.

Definitely there are more of these ones around, but the question becomes which numbers that may have such factors and which way you are able to find them as well.

[url]http://factordb.com/index.php?id=1100000000763138602[/url]

Oh, a couple of more factorizations I have stored away.

I could well upload it, but if so, don't jump your seat.

Because in fact, I was able to find a couple of better ones here.

A question for you.

This number

[url]http://factordb.com/index.php?id=1000000000000034560[/url]

possibly had a small update to it today.

Compare with this number

[url]http://factordb.com/index.php?id=1100000000775348918[/url]

which was a C207 a little while ago.

This number is not that easy to factorize. Still, the answer apparently is known here.

If you are supposed to be proud at what you are able to do, why not have it shown up where it is needed?

Really, this result is an example of trial division being carried out on a given number.

This is being done because processing power has incresead in recent times and what earlier appeared to be prime numbers, now more becomes only factors instead.

Anyway, could finish up this factorization when first at it.

Down to a C104 for this number right now, but need to go out for shopping before continuing here.

Edit: It ran off before finishing up. Redoing it right now.

[QUOTE=storflyt32;400304]This number

[url]http://factordb.com/index.php?id=1000000000000034560[/url]

possibly had a small update to it today.[/QUOTE]

Look again

Tested out the mentioned C207 manually by just dividing the numbers, but for now Yafu says 7.76 hours more to go on the remaining C144.

I will perhaps get some answers to these numbers later on.

[QUOTE=storflyt32;400314]Tested out the mentioned C207 manually by just dividing the numbers, but for now Yafu says 7.76 hours more to go on the remaining C144.

I will perhaps get some answers to these numbers later on.[/QUOTE]

Check again.

Thank you for doing that.

To people like me who are not supposed to be hacking and cracking numbers or at least codes, they become only a small part of a big puzzle.

Came across a YouTube video while looking for other contents.

[url]https://www.youtube.com/watch?v=KmIDluvVZ2M[/url]

Worth watching.

Came across this C103 a couple of days ago.

5257580682287346125119700202910679229423527432847302135626002052012162827616986817714988158206959997053

If you wish, you may give it a try. Possibly not the easiest number to factorize.

[QUOTE=storflyt32;400632]Came across this C103 a couple of days ago.

5257580682287346125119700202910679229423527432847302135626002052012162827616986817714988158206959997053

If you wish, you may give it a try. Possibly not the easiest number to factorize.[/QUOTE]

What is special about this number? An arbitrary C103 number can be factored using GGNFS in under 1 hour on a modern 4-core CPU.