I take a known prime and prove it to be a composite (..or maybe need help?)
 

In the news:

[URL]http://www.fermatsearch.org/news.html[/URL]

Scroll down towards the bottom (maybe some 5 pages up when using 1024*768 resolution).

June 23, 2011
New Fermat factor discovered after 1 day!
7333*2^138560+1

Apparently not a prime number or factor on my computer when using the ecm command on a batchfile of this number.

Rather, a C41715 instead.

Also, Yafu's isprime command is telling me the same thing.

Would someone perhaps make the time at checking?

Thanks!

Edit: Tried reporting the file at factordb using Auto detect(slow).

It did not work, so I tried Yafu(output) instead from the pull-down box.

Now it is being listed there as being a prime.

Perhaps I should give it it a try using WinPFGW as well.

Still having the assumption that this number may be a composite one.

Factordb [URL="http://www.factordb.com/index.php?id=1100000000423216548"]says[/URL] prime

[QUOTE=storflyt32;385572]7333*2^138560+1

Apparently not a prime number or factor on my computer when using the ecm command on a batchfile of this number.

Rather, a C41715 instead.
[/QUOTE]
It is a prime number. You just don't know how to use the tools that you claimed to have used.

That day again.

Want to know a little more about me?

[URL]http://www.primegrid.com/show_user.php?userid=12041[/URL]

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

You see, I am not a total newbie to this stuff.

Probably stepping on someone's toes anyway.

Having used these tools for some time now, I find Yafu to be quite accurate when it comes to the results.

I do have the ecm output. It became a little large, but it says composite for this number.

Possibly the number itself is a wrong one. I could go back and make a check once again.

Thanks!

Have done a re-check creating a new file with Yafu's ecm command using the number 7333*2^138560+1.

The number starts with 3814 and ends with 009.

Still getting a C41715 on this number.

I am moving this discussion to "Homework help".
It has nothing to do with new Fermat Factors.

If you take a hammer and a screw, hammer the screw into the wall and declare: "the hammer is not working and the screw is all bent", -- this whole thing only demonstrates that you use a hammer where you need a screwdriver.

[QUOTE=storflyt32;385580]Have done a re-check creating a new file with Yafu's ecm command using the number 7333*2^138560+1.

The number starts with 3814 and ends with 009.

Still getting a C41715 on this number.[/QUOTE]

Perhaps this discussion could be moved somewhere else as it seems to be only remotely connected with new Fermat factors (I always get excited when there is new posts in this thread...)

You are right with the start and beginning of the number... But I don't see why you would first of all use Yafu for this, and secondly, why you would post something like this in this thread before double-checking with more "standard" programs like pfgw. They do say that the number is prime (you can also write your own program to N-1-test this, if you don't trust others codes).

Edit: I see Batalov was faster than fast. Thanks!

@storflyt32: There's a motto in perl, "[URL="http://en.wikipedia.org/wiki/There%27s_more_than_one_way_to_do_it"]there's more than one way to do it[/URL]". It is applicable not only to perl, it is a philosophical thing.

Let's have a look at some ways to address the primality of this number.
Most straightforward ones (they are essentially the same) are
> pfgw -f1 -t -q"7333*2^138560+1"
> sllr64 -d -q"7333*2^138560+1"
and observe the output.

There are more ways, but these will suffice for now. Now, how about not obviously wrong ways to do it? Using ECM is like using a hammer for screws - it is for factoring, [B]not [/B]for primality checks. Using yafu is questionable because this number may be too large for it. (yafu stands for "yet another [B]factoring [/B]utility", too.)

With pfgw, however, you can [B]also [/B]check that this number indeed is a Fermat factor:
> pfgw -f1 -gos2 -q"7333*2^138560+1"
and observe.
With LLR you can do other specialized tests as well. Every tool has its own nice features. The LLR's code (at least to me) is more convenient for trying out even newer stuff; e.g. DividesPhi() test (for which otherwise you would use Proth.exe, but it is rather slow); or a test of primality of Phi(3,N)-type of numbers or many other things.

But then of course, there's this "religious belief" problem: that's all fine and well as long as we [I]believe [/I]that these tools [I]do[/I] work properly. One has two choices: believe this for granted (and there is no good reason not to: the authors are known for high quality code and frequent updates and patches when needed) [I]-or-[/I] do the check from scratch. The second approach is great, but requires learning. One half way attempt is to believe that the numeric library is not broken, and then code your own test, using libgmp/libmpir, or use Pari (which in turn will use libgmp/libmpir for you) and implement the test from known theorems. But the chain of belief doesn't end here -- you may question the validity of theorems, too. Well, then you have to read a good textbook and see how the proof and constructed and see that it is correct.

If the question of where the chain of beliefs ends for most people interests you, pick up a good textbook on social psychology. In short, outside math, the human logic proof chains are never complete for any non-trivial question. In math, you can track down the chain of proof to axioms, but elsewhere you can only check the proof chain deep enough and while parsing the argument you can also check that the argument is valid and sound. Anyway, that's a whole different story. But in this context, your argument that "my computer has this-or-that number of credits on PrimeGrid, therefore I know about math", for example, is not a sound argument. It is non-sequitur. ("I have apples, therefore I know about oranges.")

[QUOTE=Batalov;385584]"[URL="http://en.wikipedia.org/wiki/There%27s_more_than_one_way_to_do_it"]there's more than one way to do it[/URL]". It is applicable not only to perl, it is a philosophical thing.


In math, you can track down the chain of proof to axioms, but elsewhere you can only check the proof chain deep enough and while parsing the argument you can also check that the argument is valid and sound.[/QUOTE]


Good post

[QUOTE=Batalov;385584]. But in this context, your argument that "my computer has this-or-that number of credits on PrimeGrid, therefore I know about math", for example, is not a sound argument. It is non-sequitur. ("I have apples, therefore I know about oranges.")[/QUOTE]

It also earns a fair number of points on the John Baez crankometer.

[QUOTE=Batalov;385584]
Let's have a look...[/QUOTE]
:goodposting: Very good, instructive, post. :tu:

Continue right here?

I happen to know that the ecm and factor commands is about factorization.

But you may find the isprime command being included in Yafu as well.

Is this command also based on the factorization algorithm, or is it rather based on LLR?

Software like WinPFGW is doing the similar thing by means of the LLR algorithm, which by some people may be regarded as an "approximation" to a given problem.

The question becomes then. Is it all about the number being processsed (including its possible size) and also what kind of computer that is being used? Also the question about which kinds of software (including version numbers) that are being used for a given task.

Is it more likely that a PRP5463 or PRP11943 is more likely to be accepted as being such a number using either Yafu or WinPFGW? Of course you should not able to factorize a 351,639 digit number like (2^1168183-1)/54763676838381762583.

[URL]http://donovanjohnson.com/mersenne.html[/URL]

It took me 5 minutes to locate this number despite not having it here locally. You do not need a paper-based map or dictionary anymore. You are able to find almost everything you want with your PC alone.

I am also having a look at similar numbers like 7333*2^138560+1 (both with -1 and +1) that are roughly the same size.

According to [URL]http://www.factordb.com[/URL] there are other numbers still listed as "U" being of similar size as this number.

So the conclusion may be that this is still an open question lacking a finite answer.

You really should not be using yafu for primality or even prp checks of numbers this large.

However there is something interesting here:

[CODE]
int r;
mpz_t a;
mpz_init(a);
mpz_set_ui(a, 1);
mpz_mul_2exp(a, a, 138560);
mpz_mul_ui(a, a, 7333);
mpz_add_ui(a, a, 1);
printf("testing ...%lu\n", mpz_tdiv_ui(a, 1000000000));
r = mpz_probab_prime_p(a, 1);
printf("result is %d\n", r);[/CODE]

Linking with gmp 5.1.1 I get:
[CODE]testing ...112555009
result is 0
[/CODE]

Linking with gmp 4.3.2 I get:
[CODE]testing ...112555009
result is 1
[/CODE]

Bug in gmp 5.1.1?

Good post there, Batalov!

Ok, after more checking I guess it's just yafu's use of gmp-5.1.1 that is messed up somehow. After remaking gmp-5.1.1 everything worked fine (result returned PRP).

Ah. I was just about to ask if it fails for smaller inputs... Works fine here with 6.0.0.a ...
[CODE]#include <stdio.h>
#include <gmp.h>

main()
{
int r;
int i, n[5] = {5774, 7932, 21704, 24976, 138560};
mpz_t a;
mpz_init(a);
for(i=0;i<5;i++) {
mpz_set_ui(a, 1);
mpz_mul_2exp(a, a, n[i]);
mpz_mul_ui(a, a, 7333);
mpz_add_ui(a, a, 1);
printf("testing 7333*2^%d+1 [...%lu]\n", n[i], mpz_tdiv_ui(a, 1000000000));
r = mpz_probab_prime_p(a, 1);
printf("result is %d\n", r);
}
}[/CODE]

With he mpz_probab_prime_p function you need a much bigger number than 1 as the second parameter for a big number like: 7333*2[sup]138560[/sup]+1.

[CODE]int mpz_probab_prime_p (const mpz t n, int reps) [Function]
Determine whether n is prime. Return 2 if n is definitely prime, return 1 if n is probably
prime (without being certain), or return 0 if n is definitely composite.
This function does some trial divisions, then some Miller-Rabin probabilistic primality tests.
The argument reps controls how many such tests are done; a higher value will reduce the
chances of a composite being returned as “probably prime”. 25 is a reasonable number; a
composite number will then be identified as a prime with a probability of less than 2−50
.
Miller-Rabin and similar tests can be more properly called compositeness tests. Numbers
which fail are known to be composite but those which pass might be prime or might be
composite. Only a few composites pass, hence those which pass are considered probably
prime.[/CODE]

Here is Thomas R. Nicely's page on the mpz_probab_prime_p pseudoprimes in earlier versions of GMP. They seem to change the bases a bit for the Miller-Rabin tests between versions, so that is probably why you get different results in different versions.
[URL="http://www.trnicely.net/misc/mpzspsp.html"]http://www.trnicely.net/misc/mpzspsp.html[/URL]

[QUOTE=ATH;385619]With he mpz_probab_prime_p function you need a much bigger number than 1 as the second parameter for a big number like: 7333*2[sup]138560[/sup]+1.

[CODE]int mpz_probab_prime_p (const mpz t n, int reps) [Function]
Determine whether n is prime. Return 2 if n is definitely prime, return 1 if n is probably
prime (without being certain), or return 0 if n is definitely composite.
This function does some trial divisions, then some Miller-Rabin probabilistic primality tests.
The argument reps controls how many such tests are done; a higher value will reduce the
chances of a composite being returned as “probably prime”. 25 is a reasonable number; a
composite number will then be identified as a prime with a probability of less than 2−50
.
Miller-Rabin and similar tests can be more properly called compositeness tests. Numbers
which fail are known to be composite but those which pass might be prime or might be
composite. Only a few composites pass, hence those which pass are considered probably
prime.[/CODE]

Here is Thomas R. Nicely's page on the mpz_probab_prime_p pseudoprimes in earlier versions of GMP. They seem to change the bases a bit for the Miller-Rabin tests between versions, so that is probably why you get different results in different versions.
[URL="http://www.trnicely.net/misc/mpzspsp.html"]http://www.trnicely.net/misc/mpzspsp.html[/URL][/QUOTE]I suggest that 2 is "much bigger" than 1 for almost all purposes.

To see why, read up on the likelihood of the M-R test being mistaken for randomly chosen bases and randomly chosen numbers to test. If you chose the test number with malicious aforethought then, indeed, 25 tests may be appropriate. Such numbers are vanishingly rare.

Paul

This function (let's say called with 25 trials), of course, depending on the changing implementation can return a different (internal) chain of 1s, and then finally a 0 (which it will return) -- but only for a composite input. What it cannot do is return a 0 for a prime input. (which is what B.B. properly flagged as a bug. Then, it turn, even if the function is coded correctly, there are ways to miscompile, and that is what appears to be what he later diagnosed.)

For this input, one would expect an infinite row of "1"s returned (probable prime); the reason why Ben coded (...,1) was that it is quite slow for even a single M.-R. test. (~15 minutes on a fast core; pfgw takes 15 s, because it plain GMP uses a general version of multiplication and pfgw, a special fast one)

Please see this thread.

[URL]http://mersenneforum.org/showthread.php?t=14249[/URL]

If you do not mind, often a smaller number may be harder to factorize than a larger number.

The reason for this is that the factors are more equal in size to each other.

Knowing that a P8 like 36085879 is a factor of 2^333-1 is no problem, but factorizing a composite number like
293155093804870332610909957481872064551757337569254797370666783 is a little bit harder to do.

Please have me excused, but those numbers ending with -1 in the syntax definitely are a little more easy to be dealing with.

The biggest prime number that is currently known is a Mersenne prime.

Compare with the similar or corresponding Fermat search.

Right now, the largest known Fermat prime is 475856^524288+1 which is a quite bit smaller number than Mersenne48 (or M48).
So, before I started to get a hand on this stuff, I was wondering why such a prime number like the one mentioned above
is that little bit larger than the largest known fermat "factor".

[URL]http://factordb.com/index.php?query=2%5E2048%2B1[/URL]

The P564 at the right in that listing.

What is the possible relationship between these two numbers?

Is it possible to assume that a number containing some 2,976,633 digits itself might be a factor of some other even larger number (which then becomes a composite one)?

No reason to doubt why doing this kind of stuff is supposed to be a little hard to do at times.

Because you are unable to factorize such a number (like the remainder of 2^4096+1 or 2^8192+1), you do not know what the
factors are. The question becomes - is it possible to relate a specific number (factor) to a particular set of prime types?

Looking at it, I get the feeling that there may be a correspondence or relationship between a Genefer number and a rep-digit number.

Your opinion on this, please.

Thanks!

[QUOTE=storflyt32;385718]
Knowing that a P8 like 36085879 is a factor of 2^333-1 is no problem, but factorizing a composite number like
293155093804870332610909957481872064551757337569254797370666783 is a little bit harder to do.
[/QUOTE]

[code]? factor(293155093804870332610909957481872064551757337569254797370666783)

[6951431036147505831119048893 1]

[42171905652298228542447931081982731 1]
[/code]

[QUOTE=storflyt32;385718]... numbers ending with -1 in the syntax definitely are a little more easy to be dealing with.

The biggest prime number that is currently known is a Mersenne prime.

Compare with the similar or corresponding Fermat search.

Right now, the largest known Fermat prime is 475856^524288+1 which is a quite bit smaller number than Mersenne48 (or M48).
So, before I started to get a hand on this stuff, I was wondering why such a prime number like the one mentioned above
is that little bit larger than the largest known fermat "factor".[/QUOTE]
You may want to read this introduction: [url]http://primes.utm.edu/prove/[/url] (the whole set of linked pages, not just that page ;-)
It will become clear why most known giant primes are either ...-1 or ...+1.

[QUOTE=storflyt32;385718]...Because you are unable to factorize such a number (like the remainder of 2^4096+1 or 2^8192+1), you do not know what the
factors are. The question becomes - is it possible to relate a specific number (factor) to a particular set of prime types?[/QUOTE]
The b^n+-1 numbers do have very special factors (of special restricted form). This is true for Mersennes and Fermats, but also true for generalized Fermats, and (further generalized) cyclotomic numbers.

Read, the read some more, and you questions will be answered. Don't expect someone to stand by and be ready to answer your (so far, pretty basic) questions. "Give a man a fish... Teach a man to fish..." that sort of thing.

Thanks for the link.

[QUOTE=storflyt32;385718]Right now, the largest known Fermat prime is 475856^524288+1 which is a quite bit smaller number than Mersenne48 (or M48).[/QUOTE]

Hmm ... I was under the impression that 65537 is the largest known Fermat prime, but hey, what do I know?

@ ewmayer

I guess you certainly know this already.

Here is the general syntax when it comes to the Fermat numbers and their possible factorization.

2^0 + 1 = 2
2^1 + 1 = 3
2^2 + 1 = 5
2^4 + 1 = 17
2^8 + 1 = 257
2^16 + 1 = 65537

These numbers are the six first and only known Fermat factors which are known to be prime.

They are designated F(0) through F(5), respectively.

Try using for example F(6) in the input box at factordb.com (and not the web-browser address bar) and press the "Factorize!"-button.

2^32 + 1, 2^64 + 1, 2^128 +1 and 2^256 + 1, 2^512 + 1, 2^1024 + 1 and 2^2048 +1 are known to be composite numbers as a whole,
although they have now been completely factored.

But when it comes to 2^4096 + 1, 2^8192 + 1, 2^16384 + 1 and 2^32768 + 1 and so on, these numbers are only partially factored
for now, meaning that there is a mix or combination of prime factors and a remaining composite part which has yet to be factorized.

Finding the remaining factors of these numbers apparently is not a trivial manner. First a factor which is somewhere between 54 digits

(P54 = 568630647535356955169033410940867804839360742060818433)

and less than about

(2^4096+1)/25860116183332395113497853167940236083358054650286886725246241569916604094012679963198712829716480001

(which is the syntax for the C1133),

has to be found and it needs to be divisable from both 2^4096+1 and the C1133 mentioned above in order to become a valid factor.

The question becomes - in which way is this supposed to be working?

For now I really don't know the answer to this question and I have tried it out a couple of times.

Here is another example:

[URL]http://factordb.com/index.php?query=3059328257448451012124528914924445459289472845506271570768416772257721865362447461948849641168439486188201742608695176185034167120620937263286034904233584751954360912650820750922532773634896817894712355879514579840739[/URL]


The factors are already individually known, but apparently some 76.5 hours more to go in order to possibly factorize this number:

Here are the factors for this number:

P46 = 7774289568841054467342907020273258993552032567

P171 = 39351869136828636825562309706971225245700129962404540849168691727314561178481864067
5586069862814412735711970194801864005631730155162613125109843290448727462456016513851317

[QUOTE=storflyt32;386329]@ ewmayer

I guess you certainly know this already.[/QUOTE]
Do you realise who you are talking to?

[QUOTE]Here is the general syntax when it comes to the Fermat numbers and their possible factorization.

2^0 + 1 = 2
2^1 + 1 = 3
2^2 + 1 = 5
2^4 + 1 = 17
2^8 + 1 = 257
2^16 + 1 = 65537

These numbers are the six first and only known Fermat factors which are known to be prime.

They are designated F(0) through F(5), respectively.[/QUOTE]It really isn't a good idea to start inventing your own notation. You should use the standard terminology and then everyone will know what you are talking about.

The numbers in your list above, with the exception of the first one, are Fermat numbers (not Fermat factors).
Remove the first one which does not belong in the list, then the remaining numbers are [TEX]F_0[/TEX] through [TEX]F_4[/TEX]. The Fermat number [TEX]F_n[/TEX] is [TEX]2^2^n+1[/TEX].

Sorry, should have skipped the 2.

BTW: Was replying to ewmayer. Should be readily visible.

Anyway, I now have the output here for the mentioned 7333*2^138560+1 .

If this number was a prime number, it should definitely be showing up, but it does not do so.

What if I update the factordb with the most recent result and let you know?

Edit: And this is something which I am apparently not able to do.

Trust the numbers (meaning results).

[QUOTE=storflyt32;386345]Anyway, I now have the output here for the mentioned 7333*2^138560+1 .

If this number was a prime number, it should definitely be showing up, but it does not do so.

What if I update the factordb with the most recent result and let you know?

Edit: And this is something which I am apparently not able to do.

Trust the numbers (meaning results).[/QUOTE]

Output from what? Show up where? What recent result?
Your comments are so general that it's hard to figure out what you are talking about, trying to do, or not understanding from the lengthy advice you have been given in this thread.
The number you refer to is prime, and has been known to be prime for a while- so there is nothing to update in factordb or anywhere else. You have discovered nothing new about this number, but you have surely discovered which tools don't work for numbers this size.

[QUOTE=storflyt32;386329]@ ewmayer[/QUOTE]
[URL]http://www.ams.org/journals/mcom/2003-72-243/S0025-5718-02-01479-5/S0025-5718-02-01479-5.pdf[/URL]

:whistle:

[QUOTE=storflyt32;386329]@ ewmayer

I guess you certainly know this already.[/QUOTE]Yeah, exactly. I doubt ewmayer could tell the difference between Pépin's test and a pregnancy test. You tell him dude. :boxer:

Thank you very much!

Including [URL]http://factordb.com/index.php?query=3289018909828839950285397233495375495312608729711519999908385629462589823501707053451816348898028195709146280381194398910952848236577722255912280830117106073745410924257454722225416180933818531872928654602163702255020504550525896713971683343306725862850881[/URL]


Reading the .pdf right now, by the way.

You do not have to post or update this one if you wish not to do so, but this number:

[URL]http://factordb.com/index.php?query=10543858099141793567633706165613456571488994021324464032184255388501735734830314244716706835906749187785349381054183287392145341367842938953708368214292103334328105248332619908403542418842578894856690780599845067603784321027354628942698284377316441276634934880201623667710496773929693357694193269051422249268025368211692151585189681074812700784597020009094761047486927562009119226854561099845456510080977130753090111834123396116614031339670717428868049615591632090459747677046286964578601983401366511046242168546147768383690899516261551099472238446079243800103410549239830923104465229408541903281612612851226720768200137636245559187801381888198683544007019417707419456721148906013839302279348089558110191155943197067173948849807156235238157662844920262390207716107361825364483070705440058534429259974094029475525202297663281509918939435399944237755058601170817571788095655119835981550745773303862840478605165095551231145272355473159791462857543343159034190018602967650306257601279230308480192009040129237[/URL]


has then the two factors

[URL]http://factordb.com/index.php?query=393518691368286368255623097069712252457001299624045408491686917273145611784818640675586069862814412735711970194801864005631730155162613125109843290448727462456016513851317[/URL]

and

[URL]http://factordb.com/index.php?query=26793792341807736634989996206703221928991974551245243656608357295705957662434910993643582652735889417114477578195143305386606165633460494479352618199027436253125675855298638156898862031234291454088819107336178258992586290735281701539436654426222016224877857981627455730618970402046410998073275965537433922830595878994170968342869032386464859697352301955142765924502144312285624617397751070093352625339376546895701802356390969877934653964801145307320505921478365986799435114748798120051403951756511452487507878545576504672167732467680117932062327299154686527365885435933234831102575520705134772227077571687294915880830214822585884390631938094801973796975327038072799759540642174453561362916450601573932599514869012246747271586372225973769612485189642375073189717303788897993289702939522295629255121309853562659549833018243089817881761[/URL]

respectively.

Too late to edit my last post.

Anyway, also this (the main numbers themselves):

[URL]http://factordb.com/index.php?query=36577280830440033944220171233825340128191154303123031915613627190300255639397772638077174547474291780661500909153688079[/URL]

is a factor of

[URL]http://factordb.com/index.php?query=14393843686205069029433870551110062210968123715413720892050244472878272959059310794004361666620606785616621485412313879384626108246752317045329297596964813342422095090317940321072521970176937140590298812140742740719395344357688334023030836971057436946090572500357063405327086353238801350043[/URL]


Perhaps not needed?

[QUOTE=storflyt32;386356]Reading the .pdf right now, by the way.
[/QUOTE]
(channeling my internal RDS): I devilishly assume that the idea was you only read the authors' names, and realize that you are trying to sell your rotten tomatoes to very skilful and experimented gardeners. About reading the pdf, according with the quality of your post we really doubt you can do that... :razz:

Press More Information on the first link.

I think it better could show up there that this number is a composite factor (or part of) the second link, because it divides.

Thanks!

Just a little note, because it is getting late here.

While I am still sitting at my desk, I am wondering about this little thing.

I do not know whether or not someone told me so, but I was giving the impression or feeling that the subject of dealing with numbers is the science of the "poor".

Replace "poor" with something else if you wish, but I made a search on Wikipedia on the word "operand".

[URL]http://en.wikipedia.org/wiki/Operands[/URL]

Having a quick look at this article, a couple of things are missing out here.

The most important thing missing is the subject related to division.

You may be familiar with the terms and definitions being used or put up when an article does not meet the desired criteria.

As you mathematicians should know very well, the operations dealing with addition, subtraction and multiplication are supposed to be working out correctly.

But not so when it comes to division.

Take 7/3 for example. Using whole numbers should return 2 as the result. Eventually it becomes 2.33333...

The difference between 2 and 2.33333... is the error rate when it comes to division. For the division of much larger numbers, the error rate may become significantly larger.

Maybe it should read 2,33333... for clarity.

So, by comparison, dividing 35 with 5 gives 7 in return.
Multiplying 7 with 5 gives 35.

Similarly, dividing 35 with 7 gives 5 in return.
Multiplying 5 with 7 gives 35.

Is it always that easy?

"error rate"? You have been warned once in this thread to stop making up your own notation; I suggest you also stop making up your own terms, particularly when your definition of them amounts to the example you give.

You declared "using whole numbers", and then "eventually it becomes". Eventually? how does time pass in any way when discussing arithmetic? Whole numbers "become" decimals?

Division is not closed on whole numbers. Division is closed on rationals (except for divide-by-zero, obv). It seems that you are complaining division is flawed because you've chosen a set that it is not closed over. So what?

Did not mean to be rude. Only one bottle of beer and some potato chips before going to bed last night.

Perhaps better write a sentence or paragraph in the previous post this way instead.

As you mathematicians certainly know very well, the operations dealing with addition, subtraction and multiplication are supposed to be working out correctly.

Before I continue, I made some updates on 10^4032-1 in the factordb last evening.

Hope this shows up there.

When I was a little younger, I was having a pocket calculator that was able to display some 8 digits in the display.

Quite often the result of an operation ended up with the letter "E" at the right, perhaps lower bottom of the display.

At that time I interpreted this "E" as meaning or implying "Error".

One such example is division by zero (0).

Becoming a little more mature, I have been able to learn that this in fact means Infinity ("~").

Infinity in fact means something (a number) which is undefined.

[URL]http://en.wikipedia.org/wiki/Infinity[/URL]

Try using Windows Calculator with the standard "Degree" setting for the trigonometric functions.

Input 90 and choose / select the tan() function or key.

The result of this operation is another example of "Infinity".

The number being returned becomes undefined.

Since numbers may be both positive and negative, you may also be able to define a negative "Infinity" - number.

The opposite goes for the number 0.

You may be able to define an "Infinitesimal" small number, but in such a case it rather becomes
(+)0.00000000....00001, or -0.00000000....00001 instead.

[URL]http://en.wikipedia.org/wiki/Infinitesimal[/URL]

As mentioned, replace 0.00 with 0,00 if this suits you better.

BTW: One little thing to mention.

When I write this post, I do not have the scroll up/down box at the right when the text (the number of lines) becomes longer than the size of the box.

A small annoyance in an otherwise great web-page.

For now I have to press CTRL-HOME or CTRL-END in order to get to the top/bottom of the text.

Edit: Apparently fixed.

Dear storflyt32,

it is wonderful to see that you are developing many of the fundamental steps in abstract thinking (probably in a similar way that I and many others have gone through these in our youth. I still recall with warmth the (re)discovery of complex numbers, Riemann sphere etc. in the elementary school by wondering about square-roots of negative numbers and infinity.) However, for the most of the readers of this forum your observations will seem trivial and thus are hardly appreciated. Some might even call you with bad names because of this.

I do not wish to discourage you, but maybe you could concentrate more on thinking about this stuff, reading books or wikipedia on this stuff, talking with friends and relatives (if they can take it) and enjoying your discoveries... we all agree they are fantastic! [SIZE="1"](just don't write about them).[/SIZE]

Hi, rajula!

Thank you for mentioning / suggesting the term "abstract thinking".

I shall be looking it up.

Edit: More here.

[URL]http://en.wikipedia.org/wiki/Abstract_thinking[/URL]

Have not read it yet.

[URL]http://factordb.com/index.php?query=45629566105789425350275021920015123621770407143528500714049525955646634476732429688397036395803670164293742312328034451177219063420208650356477519060825706225303929109492562233810289745687336928610630591031896947667470094702213135161082147761577695892993981561125237422095824991625334565127507075502559661927403509543875063532403654530763764126828623964060386804102566409362791327521742800050805262372105342592833936637349816394615124263630866678263789379833621473996917435576445120589046042043668280748371665793378681[/URL]
[URL]http://factordb.com/index.php?showid=1100000000723307189[/URL]
45629566105789425350275021920015123621770407143528500714049525955646634476732429688397036395803670164293742312328034451177219063420208650356477519060825706225303929109492562233810289745687336928610630591031896947667470094702213135161082147761577695892993981561125237422095824991625334565127507075502559661927403509543875063532403654530763764126828623964060386804102566409362791327521742800050805262372105342592833936637349816394615124263630866678263789379833621473996917435576445120589046042043668280748371665793378681
C 518 (show) 4562956610...81<518> = 4562956610...81<518>

[URL]http://factordb.com/index.php?query=393518691368286368255623097069712252457001299624045408491686917273145611784818640675586069862814412735711970194801864005631730155162613125109843290448727462456016513851317[/URL]
[URL]http://factordb.com/index.php?showid=1100000000716666264[/URL]
P 171 (show) 3935186913...17<171> = 3935186913...17<171>
393518691368286368255623097069712252457001299624045408491686917273145611784818640675586069862814412735711970194801864005631730155162613125109843290448727462456016513851317

[URL]http://factordb.com/index.php?query=115952728819901507458166387237485521241477795414849559021457137148634864009879070236848874957279231891557575945967709239155558147675198763716668975148823497966114660403171775054227401855658787987518283647785074569363972355151586812277834981875328066633865140192392195632056010493622564741857124405112070535514914383391682856842412807108234773648693[/URL]
[URL]http://factordb.com/index.php?showid=1100000000723307203[/URL]
P 348 (show) 1159527288...93<348> = 1159527288...93<348>
115952728819901507458166387237485521241477795414849559021457137148634864009879070236848874957279231891557575945967709239155558147675198763716668975148823497966114660403171775054227401855658787987518283647785074569363972355151586812277834981875328066633865140192392195632056010493622564741857124405112070535514914383391682856842412807108234773648693
- - -
[URL]http://factordb.com/index.php?query=3106813337466386245901867721801754771887327565922746669951959154873468110801292589233810050404320090663701785937700569108146409680058835566712225655240451504153631729474248532907179609691538202655989811577409833805879338674829461631494199095393812745141778803344900395181048096307686461368863941578920432813053194954203166240311484605521959759922445977821711269282527974517760419145125740169079941898692091774481300709196471121509701488606767661802672451412806199875386698299141137325319346127327741652944626014089253209726141986802232494715135444932178873464258650173215507053312459481059188993085960760997040971600872758525878507323394782833261712609904617230487820723843772720380492409188243708908800551670914484261935857245949199891801826952811781825460477938660021422352279220982260130781355092005548881884024438263354434966091867710076423271179673244299386023313173285154856427365591354996717332792391414582081243977207782642930598327762950203864414602117614748097776833056459062769555898113671862751576927328547367390836604790454747959076340878101219416618620664944941037019552123829534006240056954596292388063721010607482342178473469230844101853114593473335405906426188373[/URL]
[URL]http://factordb.com/index.php?showid=1100000000721260791[/URL]
C 1180 (show) 3106813337...73<1180> = 3106813337...73<1180>
C 1180 (show) 3106813337...73<1180> = 3106813337...73<1180>
3106813337466386245901867721801754771887327565922746669951959154873468110801292589233810050404320090663701785937700569108146409680058835566712225655240451504153631729474248532907179609691538202655989811577409833805879338674829461631494199095393812745141778803344900395181048096307686461368863941578920432813053194954203166240311484605521959759922445977821711269282527974517760419145125740169079941898692091774481300709196471121509701488606767661802672451412806199875386698299141137325319346127327741652944626014089253209726141986802232494715135444932178873464258650173215507053312459481059188993085960760997040971600872758525878507323394782833261712609904617230487820723843772720380492409188243708908800551670914484261935857245949199891801826952811781825460477938660021422352279220982260130781355092005548881884024438263354434966091867710076423271179673244299386023313173285154856427365591354996717332792391414582081243977207782642930598327762950203864414602117614748097776833056459062769555898113671862751576927328547367390836604790454747959076340878101219416618620664944941037019552123829534006240056954596292388063721010607482342178473469230844101853114593473335405906426188373

[URL]http://factordb.com/index.php?query=115952728819901507458166387237485521241477795414849559021457137148634864009879070236848874957279231891557575945967709239155558147675198763716668975148823497966114660403171775054227401855658787987518283647785074569363972355151586812277834981875328066633865140192392195632056010493622564741857124405112070535514914383391682856842412807108234773648693[/URL]
[URL]http://factordb.com/index.php?showid=1100000000723307203[/URL]
P 348 (show) 1159527288...93<348> = 1159527288...93<348>
115952728819901507458166387237485521241477795414849559021457137148634864009879070236848874957279231891557575945967709239155558147675198763716668975148823497966114660403171775054227401855658787987518283647785074569363972355151586812277834981875328066633865140192392195632056010493622564741857124405112070535514914383391682856842412807108234773648693

[URL]http://factordb.com/index.php?query=26793792341807736634989996206703221928991974551245243656608357295705957662434910993643582652735889417114477578195143305386606165633460494479352618199027436253125675855298638156898862031234291454088819107336178258992586290735281701539436654426222016224877857981627455730618970402046410998073275965537433922830595878994170968342869032386464859697352301955142765924502144312285624617397751070093352625339376546895701802356390969877934653964801145307320505921478365986799435114748798120051403951756511452487507878545576504672167732467680117932062327299154686527365885435933234831102575520705134772227077571687294915880830214822585884390631938094801973796975327038072799759540642174453561362916450601573932599514869012246747271586372225973769612485189642375073189717303788897993289702939522295629255121309853562659549833018243089817881761[/URL]
[URL]http://factordb.com/index.php?showid=1100000000716659445[/URL]
P 833 (show) 2679379234...61<833> = 2679379234...61<833>
26793792341807736634989996206703221928991974551245243656608357295705957662434910993643582652735889417114477578195143305386606165633460494479352618199027436253125675855298638156898862031234291454088819107336178258992586290735281701539436654426222016224877857981627455730618970402046410998073275965537433922830595878994170968342869032386464859697352301955142765924502144312285624617397751070093352625339376546895701802356390969877934653964801145307320505921478365986799435114748798120051403951756511452487507878545576504672167732467680117932062327299154686527365885435933234831102575520705134772227077571687294915880830214822585884390631938094801973796975327038072799759540642174453561362916450601573932599514869012246747271586372225973769612485189642375073189717303788897993289702939522295629255121309853562659549833018243089817881761

Cmd resurrected ... :cmd:

:ban:

Any idiot can take two primes of ~300 digits, multiply them, and put the result in the DB. Then post the product on the forum, without 'code' tags.

:ban:

People were banned from fdb for less... :yucky:

Is the size of a given number a problem here?

We all know that numbers like RSA-1024 and RSA-2048 can not be factorized at the present moment, because of the inherent
limitations of the software itself, as well as computer hardware and software architecture, including processor and memory.

RSA-1024 is a 309-digit number. RSA-2048 is a 617-digit number.

Definitely I respect the value these two numbers are representing by making up a code which supposedly can not be broken and right now is being represented by means of an appropriate certificate for that given purpose.

In this way information may be transferred across the web and be read and written by only two parties, namely the sender and
the receiver of a given message.

In another instance I might perhaps be dealing with a number like 10^1000-1.

By just having a look at it, I am able to see that this number is divisable by 3 and also what it becomes next.

Same goes with rep-digit numbers and the similar. They go on forever, but most of them in the end show up as composite.

So the question then becomes - where is the fun of it?

Am I supposed to be able to factorize such numbers at all, or is it possible that the result may become unknown forever?

Should I perhaps be doing something else instead?

As long as 12 divides 8 and gives 1 as the result and not 2, I most likely am stuck with what I am doing.

In the end I may be able to find a couple of factors which ends up being prime, but does it always work out for the big
number you may be testing?

Definitely science (including the science of numbers) is not infallible.

Perhaps it is time for me to find something else to do instead?

Thanks!

[QUOTE=storflyt32;386904]Perhaps it is time for me to find something else to do instead?[/QUOTE]
No, not if you're still interested. Just don't use the forum as somewhere for your random jottings, which is what your postings amount to. Please read rajula's excellent advice again.

This forum is however a good place to ask questions about where you can learn more, or to get help if you don't understand something.

[QUOTE=storflyt32;386904]Is the size of a given number a problem here?[/QUOTE]

I don't understand what you're trying to do in the first place, so I would say that -- rather than the size of the numbers -- is the problem.

Just in here to tell you that I found a PRP2036 before going to bed yesterday and was able to report it to the FDB.

Edit: Also a PRP938 just a couple of minutes ago. I am in the process of reporting it right now.

I am tempted to ask you the following question.

In some instances, numbers thought to be composite are in fact a product of large primes.

When it comes to the Mersenne numbers, both factoring and prime number finding by means of the LLR algorithm, these numbers are then called or nick-named Mersenne semiprimes.

A composite number like 1427247692705959880439315947500961989719490561 may be shown by means of proper factorization to be having the two prime factors 2305843009213693951 and 618970019642690137449562111.

These two factors, P19 = 2305843009213693951 and P27 = 618970019642690137449562111 corresponds to
(2^61)-1 and (2^89)-1 which are M9 and M10 (or Mersenne 9 and Mersenne 10), respectively.

These two factors are not that big in size. In the long run, they only become part of a larger picture in which there is a main separation or difference between prime numbers and composite numbers.

By means of doing such a thing, you will always want to know which numbers are composite and which numbers are prime. Also you would like to know in which way different numbers are linked together.

Definitely the process of factorization has its limits because of current technology. In the end we may become stuck with the general principle of multiplication and division when it comes to the handling of specific numbers.

Please, if you want help, describe your objective in as few words and as coherently as you are able. I don't think anybody really knows what you are trying to do or say. You say you have a question to ask, but you never ask it. You also ask if you should move on to other things without making it clear what it is that you are doing. First: What are you trying to do? Second: What do you want help with?

[QUOTE]In some instances, numbers thought to be composite are in fact a product of large primes.[/QUOTE]
These are still composite numbers. Semiprimes are still composite. But maybe you don't mean to suggest differently.

What are these PRPs and why are you searching for them?

The best that I can tell, you are asking if factoring and searching for primes is a worthwhile endeavor. That's up to you. The people here have made it into a hobby. If you're interested in it, pursue it. If you're not, forget about it, and count the money saved on your electricity bill. There are an infinite amount of numbers for which you will never know their full factorisations, let alone a single factor. Don't get hung up on it.

[QUOTE=storflyt32;387231]When it comes to the Mersenne numbers, both factoring and prime number finding by means of the LLR algorithm, these numbers are then called or nick-named Mersenne semiprimes.[/QUOTE]

When Mersenne numbers are proven prime with the LL (Lucas-Lehmer) algorithm, they are called "Mersenne primes" not "Mersenne semiprimes". A semiprime is a composite number with just 2 prime factors.

Oops!

My bad.

Probably what I meant to say, though.

If you don't mind, writing it in full only wastes space.

If I just provide you with a syntax, you probably would not believe me.

As an example, try multiplying

(2^57131-1)/61481396117165983261035042726614288722959856631

with

(2^63703-1)/42808417

and then try factorizing this number next.

Probably it would not be working.

But both these numbers are prime numbers individually.

In the end they become just factors.

I'm sorry, but you're not really saying anything revolutionary. Do you expect the factoring algorithms to magically and instantly know what numbers you happened to multiply together? That's not how that works. They don't instantly know what two primes you multiplied together any more than you know the precise date of my birth, or my mother's date of birth or my father's date of birth.

2 is a factor of 4. 2 is still a prime number. "Factor" does not mean "composite". [B]Every[/B] prime number is a factor of an [I]infinite[/I] amount of composite numbers. What are you trying to say? Please, provide us with a "syntax".

If you haven't done any reading on the subject, at least take a look at the first few chapters of
Hardy & Wright: Introduction to Number Theory (You can read this here: [url]https://archive.org/details/AnIntroductionToTheTheoryOfNumbers-4thEd-G.h.HardyE.m.Wright[/url])

I like videos. Though I'm sure there are better videos on the topic out there, I quite like this channel: [url]https://www.youtube.com/user/ArtOfTheProblem[/url]

[QUOTE=storflyt32;387487]
But both these numbers are prime numbers individually.
In the end they become just factors.[/QUOTE]
I had at home two molecules of apple and one molecule of beer. After I ate them, they became just diarrhoea...
Welcome back kathegetes.
(Bots today become cleverer and cleverer!)

Oh. Am I making a fool of myself, trying to talk to a bot or a troll? I was just about to give up.

[QUOTE=Jayder;387513]Oh. Am I making a fool of myself, trying to talk to a bot or a troll? I was just about to give up.[/QUOTE]

I learned something from your efforts and explanations. I was also marveling at your patience and tolerance. :bow:

[QUOTE=Jayder;387513]Oh. Am I making a fool of myself, trying to talk to a bot or a troll? I was just about to give up.[/QUOTE]
Like Kieren, I too admire your patience and tolerance. And it's always safest to assume someone is genuinely looking for help. Too often people are wrongly flagged as trolls when they are genuinely seeking help. But given the failure so far to take up or even acknowledge the help which you and various others have tried to give to the original poster in this thread, I think LaurV is right to nip this one in the bud now. But I might be wrong. It's always a very difficult call.

At some point, I don't think it matters if "storflyt32" is a person or a bot, as it seems that time-wasting and attention-getting are the main goals.

If nothing else, it may help some third party who may eventually stumble across it. So help is never unmerited :smile:

[QUOTE=Dubslow;387591]If nothing else, it may help some third party who may eventually stumble across it. So help is never unmerited :smile:[/QUOTE]

Well Put! :tu:

I don't say this guy is a bot for sure (I was just trying to throw him a trap, I have this obsession with bots, since I have some experience in this domain, working for [URL="http://en.wikipedia.org/wiki/ELIZA"]Eliza-like[/URL] stuff for a while, you may remember I accused other "forum members" too, in the past, and mostly being right), but he for sure scores very high in the list, almost as high as kathegetes, with this disparate ideas, in disparate sentences, each in its own paragraph, replying to [U]patterns[/U] in the sentences and not to the [U]idea[/U] in the sentences (here it scores very high!), etc. When you say something like "preparation is the mother of wisdom", most Eliza-beans will almost always reply with something about how clever their mothers are, or they will ask you about your parents. But some people still fall for it, for example is notorious the anecdote about the boss who came into the office in the morning and founds his secretary looking like she stayed overnight, crying in front of the computer screen, on which Eliza was running, and she told him that "nobody in her life understood her better" than Eliza did.

Patterns?

Like

4352606590838606384629892857142857142857142857142857142857142857142857142857142857142857142857142857142857
14285714285714285714285714285714285714285714285715540392101340462301 ?

BTW: Possibly a big prime number here in a randomly generated number started up directly under Windows.

If I abort the task using CTRL-C I will lose the number.

It hangs up my system quite much.

So I will have to wait for it to finish and come back to you later.

A suggestion for you:

To me the boxes for "Submit Reply" and "Preview Post" in this page could have their positions switched.

That would make it a little easier, at least for me.

Oh, sigh!

After more than 4 days of continuously running.

>> ecm(ans)

ecm: 0/1 curves on C992203, B1=11K, B2=gmp-ecm default
Aborting...

I will not be doing it this way anymore.

But otherwise, I was able to keep the last 23649 digits of this number for the record.

This number also became a composite.

What was that C992203? I didn't find it in the DB.

[url]http://factordb.com/index.php?query=68311*2%5E68311%2B1[/url]

[url]http://factordb.com/index.php?id=1100000000728640727[/url]

...814430153129546815608792557743949510056834204820738173355221

is composite: RES64: [5824C095DA4C2A85] (40.9395s+0.0096s)

[url]http://factordb.com/index.php?query=%2823*10%5E46554-11%29%2F3[/url]

Composite.

What am I missing that makes that important enough to make a post about? It takes only a few milliseconds to determine that result.

[QUOTE=danaj;388281]What am I missing that makes that important enough to make a post about? It takes only a few milliseconds to determine that result.[/QUOTE]

Is there a special form for the divisors of a number of the form a*b^c + d, in cases like this where c is relatively large?

[QUOTE=danaj;388281]What am I missing that makes that important enough to make a post about? It takes only a few milliseconds to determine that result.[/QUOTE]
You are not missing anything. The poster is an attention-seeker or a lame bot.

Tell us more about Patterns.

[QUOTE=CRGreathouse;388283]Is there a special form for the divisors of a number of the form a*b^c + d, in cases like this where c is relatively large?[/QUOTE]
Short answer: PFGW claims it can optimize this with d "up to 42-bits" but I know nothing at all about the details. My pretests are just using basic trial division (gcd for tiny primes, then simple treesieve for larger).

In the case of the composite mentioned, there is a small factor so easily caught -- it takes under 0.04s for my is_prime to find it just using simple trial division tests based on the input size. OpenFPGW and Pari/GP don't do much trial division, but still don't take very long for the first PRP test to indicate composite (~30s and 4.5 minutes respectively). If I skip the pretests and force just BPSW or base-2 SPRP it's 2.5min for ntheory (as expected, PFGW is much faster at this size).

I don't think LLR would cover this, especially not with the /3. Ignoring the /3, PFGW-3.7.7 indicates it can optimize k * b^n +/- c for c to 42-bits. I haven't looked into it at all however -- the LLR code I've added to my software is braindead simple, just doing b=2, c = -1, k = not-div-by-3. c=+1 is easily done via BLS75-T5. Riesel discusses the k-div-3 case for k*2^n-1 Bosma (1993) has some info, and there's a good post from a few years ago on this forum that has a lot of details, but I haven't gone into it (and it doesn't answer your question anyway).

Berrizbeitia et al. have a generalization to A*m^s+w where w has restrictions.

[QUOTE=CRGreathouse;388283]Is there a special form for the divisors of a number of the form a*b^c + d, in cases like this where c is relatively large?[/QUOTE]

I hope that's rhetorical if(gcd(a,d)!=1 or gcd(b,d)!=1, then gcd(a,d) or gcd(b,d) is a divsor) or a typo.

[QUOTE=science_man_88;388287]I hope that's rhetorical if(gcd(a,d)!=1 or gcd(b,d)!=1, then gcd(a,d) or gcd(b,d) is a divsor) or a typo.[/QUOTE]

In this case (a = 23, b = 10, c = 46554, d = -11) both GCDs are 1. But I'm not talking about finding a single factor but a class of factors, just like prime factors of Mersenne numbers have a special form. In this case I checked for divisibility by all small primes directly (modular exponentiation) but I wondered if there was a faster way. (I was pretty sure that there was one and that people here would know more about this than I do.)

[QUOTE=danaj;388286]In the case of the composite mentioned, there is a small factor so easily caught -- it takes under 0.04s for my is_prime to find it just using simple trial division tests based on the input size.[/QUOTE]

My experience was similar -- 57ms with modular trial division in PARI/GP*, or 92ms using a big GCD.

* Of course if I did it in PARI directly it would be a good bit faster but I just did it in gp.

[QUOTE=danaj;388286]OpenFPGW and Pari/GP don't do much trial division, but still don't take very long for the first PRP test to indicate composite (~30s and 4.5 minutes respectively). If I skip the pretests and force just BPSW or base-2 SPRP it's 2.5min for ntheory (as expected, PFGW is much faster at this size).

I don't think LLR would cover this, especially not with the /3. Ignoring the /3, PFGW-3.7.7 indicates it can optimize k * b^n +/- c for c to 42-bits. I haven't looked into it at all however -- the LLR code I've added to my software is braindead simple, just doing b=2, c = -1, k = not-div-by-3. c=+1 is easily done via BLS75-T5. Riesel discusses the k-div-3 case for k*2^n-1 Bosma (1993) has some info, and there's a good post from a few years ago on this forum that has a lot of details, but I haven't gone into it (and it doesn't answer your question anyway).

Berrizbeitia et al. have a generalization to A*m^s+w where w has restrictions.[/QUOTE]

That's interesting, but you're talking about primality/compositeness testing, while I'm talking about (partial) factorization. That is: I want the equivalent of the 2kp + 1 for Mersenne numbers, not the equivalent of LLR/BLS.

[QUOTE=CRGreathouse;388290]That's interesting, but you're talking about primality/compositeness testing, while I'm talking about (partial) factorization. That is: I want the equivalent of the 2kp + 1 for Mersenne numbers, not the equivalent of LLR/BLS.[/QUOTE]I realized that partway through writing my reply, but kept on with it anyway :down:. I claim ignorance of special factor forms, but would enjoy seeing any positive responses.

[QUOTE=danaj;388281]What am I missing that makes that important enough to make a post about? It takes only a few milliseconds to determine that result.[/QUOTE]

The last time that I dared to question the purpose of posting a result, I was (to summarize)
accused of being an asshole by Gordon in a fairly lengthy diatribe.

Allow me to point out that there has been no similar reply here.......

To be back on track: just pointing out that, according with factorDB, this number is known to be composite since (about) March 2011. As Batalov said, the guy is either innocent (in the bad sense) or a bot.

[edit: I am also interested in the discussion started by CRG's question, for some "general" case]

Quoting here.

Batalov said:

I am moving this discussion to "Homework help".
It has nothing to do with new Fermat Factors.

If you take a hammer and a screw, hammer the screw into the wall and declare: "the hammer is not working and the screw is all bent", -- this whole thing only demonstrates that you use a hammer where you need a screwdriver.

-

Oh, definitely we missed some factors between the P252 and the P564 (Fermat).

Or, what the heck else.

Getting back to it, of course.

[QUOTE=storflyt32;388372]Quoting here.

Batalov said:

I am moving this discussion to "Homework help".
It has nothing to do with new Fermat Factors.

If you take a hammer and a screw, hammer the screw into the wall and declare: "the hammer is not working and the screw is all bent", -- this whole thing only demonstrates that you use a hammer where you need a screwdriver.

-

Oh, definitely we missed some factors between the P252 and the P564 (Fermat).

Or, what the heck else.

Getting back to it, of course.[/QUOTE]


And that pretty much seals it. Bot.

:ban:

[QUOTE=TheMawn;388413]And that pretty much seals it. Bot.

:ban:[/QUOTE]

I should clarify for anyone who might be wondering about this, go back a few pages and find LaurV's explanation which is fairly good. In this case, the bot is parsing the various replies for specific words (in this case "new Fermat Factors") and constructed something that your average monkey might mistake for a valuable response.

The bot is lame so it fails to understand any meaning whatsoever from the sentence. It picked up "new Fermat Factors" from a sentence whose meaning was almost unaffected by those three words.

Because Batalov's reply was otherwise completely unrelated to the specific topic, there was nothing else within the bot's scope, so it built an entire reply off those three words, and the result is some unrelated gibberish. On top of that, failing to use our own built-in quote function (and earlier suggesting that we swap the "Submit Reply" and "Preview Post" buttons because it would be more convenient for it if they were reversed) shows that we are dealing with something that can't think.

(I guess we can't rule out a particularly stupid human being, then)

[QUOTE=LaurV;388303]To be back on track: just pointing out that, according with factorDB, this number is known to be composite since (about) March 2011. As Batalov said, the guy is either innocent (in the bad sense) or a bot.[/QUOTE]

For my part, I'd be impressed if it was a bot. It would be relatively easy for a bot to check for small or known factors, which storflyt32 tends not to do. It's hard for a bot to invent quixotic definitions for standard terms, and then explain what they mean in context. I think that storflyt32 is a human, and probably not a native English speaker.

[QUOTE=LaurV;388303][edit: I am also interested in the discussion started by CRG's question, for some "general" case][/QUOTE]

I was sort of hoping that Silverman would have put his 2 cents in. It's entirely possible that there is no special form, but I'd be more inclined to believe it if he said so.

Getting this result tonight.

If you try dividing this number:

[url]http://factordb.com/index.php?id=1100000000731307790[/url]

The C1057 at the end there:

BTW: Not the C1133 which is the composite remainder of 2^4096, but a similar, slightly smaller number.

[url]http://factordb.com/index.php?id=1100000000731307941[/url]


with this number (which is a C225)

[url]http://factordb.com/index.php?id=1100000000731295787[/url]

you will be able to get this PRP829 as a result.

[url]http://factordb.com/index.php?id=1100000000731295787[/url]

BTW, the query lines becomes a little long, so I am using the shorter syntaxes available for this instead.

The problem here is that this C225 is really a hard one to factorize. It probably has only some 2 factors rather than 3 or 4.

Thanks!

So, if you don't mind, a question for you.

In which way are you supposed to find the "next" prime in a (logical) sequence.

Take this link as an example.

[url]http://factordb.com/index.php?query=2%5E1024%2B1[/url]

Assume that I only happened to know about the three smallest factors, but not the largest one,being present here.

In which way am I able to possibly be able to find or locate this "next" prime?

Not all sequences are that logical. There may be a mix of even factors when it comes to size. In other cases there may only
be one or more small ones and perhaps a large one. Nothing in between.

Still such a number may become fully factored at times.

Thanks for any answers!

[QUOTE=CRGreathouse;388434]For my part, I'd be impressed if it was a bot. It would be relatively easy for a bot to check for small or known factors, which storflyt32 tends not to do. It's hard for a bot to invent quixotic definitions for standard terms, and then explain what they mean in context. I think that storflyt32 is a human, and probably not a native English speaker.[/QUOTE]
A bot performing like that would impress me too, but what clinches my own perceived lack of forum-integrity in storflyt32's postings is the failure to respond to what other people are saying or to interact with others at all. The English is good enough to be able to do that. If human, the motivation for the behaviour is unclear (it may be attention seeking as has been suggested, or it may be that this person just doesn't interact with others in normal life for whatever reason). But whatever the reasons behind it, the behaviour is unsuitable for an interactive forum.

I am amazed that this thread has stretched out for so many pages.

This could possibly be added under "More information" for

[url]http://factordb.com/index.php?id=1100000000720533470[/url]

is a factor of

[url]http://factordb.com/index.php?id=1100000000716659482[/url]

Please see

[url]http://factordb.com/index.php?id=1100000000716666264[/url]

for this.

- - -

Also this:

[url]http://factordb.com/index.php?id=1100000000731322732[/url]

apparently is having factor

[url]http://factordb.com/index.php?showid=1100000000731320815[/url]

This factor is only a couple of hours old, by the way.

Result listed at:

[url]http://factordb.com/index.php?id=1100000000731295787[/url]

Thanks!

[QUOTE=Brian-E;388477]A bot performing like that would impress me too, ...[/QUOTE]And I doubt that bots would edit their own posts three minutes later.

About 10 years ago I was playing some board games on a gaming site. There was a girl there who almost could sustain any conversation, play reasonable 3 or 4 different games (like gomoku, reversi, etc), participate in ad-hoc competitions, post on the forums (and edit her own posts too!). She was quite popular on the site and everybody knew her. We also learned she was a bot. The only reason we learned she was a bot, was because the author said so. Suspicion arose from the fact that she was doing the same mistakes in the games for ever and ever (her play was not randomized, she was there to talk, not to play!), and some people used her to increase their ratings on the site (playing and winning against her the same game, few times a day or so in a row). She also used to talk in 50 chat rooms (game boards) in the same time, or play 10 games simultaneously, which was really strange! And suspicious! :wink: The author of the girl sold the site for good money (and now you can only play poker and rummy and stupid games on it!) and then worked for google for a while (and "she" was one of the reasons why google took him, beside of other many nice things he did), till he found a [URL="http://www.vivi.ro/"]better life[/URL] for himself. We used to be friends once...

[edit: this is not to say that you are far behind of what the bots can do today, sorry if you feel so, but just imagine this was 10 years ago! :razz:]

Is factorization meant to be just a tool, or are you ever supposed to be able to think yourself and possibly be able to
make up your mind?

Have a look at this number and its corresponding factorization.

[url]http://factordb.com/index.php?id=1100000000647335885[/url]


This number, having the remaining composite part

[url]http://factordb.com/index.php?id=1100000000647336006[/url]


in fact divides this number

[url]http://factordb.com/index.php?id=1100000000017377290[/url]


giving me this composite number as the result.

[url]http://factordb.com/index.php?id=1100000000643754575[/url]


So to me, this number has really become fully factorized.


The remaining factor in between when it comes to these Fermat numbers is

[url]http://factordb.com/index.php?id=1100000000017315243[/url]


Really, for now the largest Fermat factors typically are not part of a given factorization.

At least it does not show up there right now in the Factor Database.


These numbers eventually becomes part of even larger number structures.

For example

[url]http://factordb.com/index.php?id=1000000000012172552[/url]

Trying out this one right now.


Therefore, several other similar examples should exist among these composite numbers.

For now the only option is to try dividing a given composite number with one of these numbers and then multiply the answer you get the opposite way in order to see whether it matches the number you started dividing from.

[QUOTE=storflyt32;388700]For now the only option is to try dividing a given composite number with one of these numbers and then multiply the answer you get the opposite way in order to see whether it matches the number you started dividing from.[/QUOTE]
I concur doctor it is a bot. :ban:
That and the evident lack of self-defense.

Let's test this hypothesis:

[QUOTE=Wiki]The following is from the noted source.[/QUOTE]
Not all numbers of a given length are equally hard to factor. The hardest instances of these problems (for currently known techniques) are semiprimes, the product of two prime numbers. When they are both large, for instance more than two thousand bits long, randomly chosen, and about the same size (but not too close, e.g. to avoid efficient factorization by Fermat's factorization method), even the fastest prime factorization algorithms on the fastest computers can take enough time to make the search impractical; that is, as the number of digits of the primes being factored increases, the number of operations required to perform the factorization on any computer increases drastically.

[QUOTE=LaurV;388303]To be back on track: just pointing out that, according with factorDB, this number is known to be composite since (about) March 2011. As Batalov said, the guy is either innocent (in the bad sense) or a bot.

[edit: I am also interested in the discussion started by CRG's question, for some "general" case][/QUOTE]


Which number, please?

I lost you here.

Thanks!

Eugene Goostman? Is that you?

[URL="http://setiathome.berkeley.edu/forum_thread.php?id=73507&postid=1508549#1508549"]This BOINC user[/URL] claims to be storflyt. Strangely, he manages to be both more comprehensible and less comprehensible in some of his posts there. Take a look at his posts on that thread. He says, "[URL="http://setiathome.berkeley.edu/forum_thread.php?id=73507&postid=1508619#1508619"]Enjoy[/URL]," and then replies to himself, saying, "Enjoying." There's reply after nonsensical reply to himself. But then comes [URL="http://setiathome.berkeley.edu/forum_thread.php?id=73507&postid=1509207#1509207"]this post[/URL], which makes a (comparatively) astounding amount of sense.

While we are suggesting bannings, can we take a vote on what human we can ban next? I've got a vote I'd like to cast. Anonymously, of course, because I'm a coward.

That is a correct assumption, but not the total answer to a given problem.

[url]http://factordb.com/index.php?id=1000000000012154120[/url]

Or, to be more precise

[url]http://factordb.com/index.php?id=1100000000212123761[/url]

You see, I fell in love with this number because there apparently is no easy way at getting to the answer of this problem.

All those composite numbers that are in between that are odd and also does not end in 5 have to be more or less factorized.

For some numbers it becomes easy. For other ones again it becomes a hard thing to do.

If I try dividing this number with another composite number, or preferably a prime factor, I eventually expect it to do so.

For now it does not do so however.

The closest we probably came here was the number 3 multiplied with 2 quite large prime factors.

Right now this number lies here on another disc which has become stuck.

Using Yafu, I try using the command ecm(ans) or ecm(ans,30) meaning a more in-depth 30-curves factorization on a given
number. You may try so on the RSA-1024 or RSA-2048 numbers as an example. You will probably not be able to succeed here.

If a given number stands such a 30 curve factorization without giving in no more, I then next try dividing this number from
the C1133.

If the number I get stands out I next try factorizing it further using the Yafu factor command.

By experience I happen to know that dividing a composite number with another composite number is not a good thing to do, but
for this C1133 which is having no known factors, there appears to be an exception for this assumption.

Usually, when factorizing the number I get, the first factor is a small one. I may get something like 4964683539819829097117,

which is a C22 that next factorizes into 61*101*293*449*1723*47701*74527.

Dividing the C1133 into this number or something else gives me a cyclic circle of mostly composite numbers that apparently
never is ending.

At times I become a little more lucky while doing so.

[url]http://factordb.com/index.php?id=1100000000732465229[/url]

My lucky one tonight.

However the P309 there does not divide neither from RSA-2048 nor the C1133.

[QUOTE=Jayder;388705]Eugene Goostman? Is that you?

[URL="http://setiathome.berkeley.edu/forum_thread.php?id=73507&postid=1508549#1508549"]This BOINC user[/URL] claims to be storflyt. Strangely, he manages to be both more comprehensible and less comprehensible in some of his posts there. Take a look at his posts on that thread. He says, "[URL="http://setiathome.berkeley.edu/forum_thread.php?id=73507&postid=1508619#1508619"]Enjoy[/URL]," and then replies to himself, saying, "Enjoying." There's reply after nonsensical reply to himself. But then comes [URL="http://setiathome.berkeley.edu/forum_thread.php?id=73507&postid=1509207#1509207"]this post[/URL], which makes a (comparatively) astounding amount of sense.

[B]While we are suggesting bannings, can we take a vote on what human we can ban next?[/B] I've got a vote I'd like to cast. Anonymously, of course, because I'm a coward.[/QUOTE]

Ooh! Let's have a lottery and stone the loser! :edit:

I was able to read Jayder's post only after posting my previous one here.

Definitely privacy is not guaranteed when you are using the web and making your voice there.

To be more precise.

I am neither of these ones. I happen to be someone else.

But start screaming. Make a fuzz out of it. Big things - small things, something for you to either enjoy or perhaps dislike.

Some people are supposed to be making science out of certain things.

Other people chooses to rather be making a sensation of it instead.

At times the true story becomes hard to believe.

A story is always supposed to be having given facts.

Are we always supposed to be believing in such stories and is it perhaps supposed to embarass or hurt at times when it possibly hits back at you?

Better have a solid heart and stomach when trying to be brave or just curious.

To late to edit. Lost my changes.

Was to say that the web also now has become an important place when it comes to both storage as well as how we are dealing with and handling the information that is now present there.

At times some early experience becomes forgotten and you only are being remindered when it for some reason happen to stumble across you once again.

Thanks to some other recent postings here I was able to retrieve a PRP948 that resulted from a factorization of a number.

Not too bad when it happens.

[url]http://factordb.com/index.php?id=1000000000045106006[/url]


C:\Users\...\winpfgw>pfgw64 -q("2^85982+1)/9300928793082484045"
PFGW Version 3.7.7.64BIT.20130722.Win_Dev [GWNUM 27.11]

(2^85982+1)/9300928793082484045 is composite: RES64: [2CFCA2741BAE4653] (21.6781s+0.0007s)

Testing "Lara".

She is supposed to be cute.

By the way, if you did not know it already, she happens to be just a bot.

Make up your own mind about the subject.

[IMG]<img src="http://i591.photobucket.com/albums/ss355/mittbilde32/r-LARA-LOGAN-large570_zps401097cf.jpg" border="0" alt=" photo r-LARA-LOGAN-large570_zps401097cf.jpg"/></a>[/IMG]

For now I am apparently not successful.

Need your suggestions when it comes to either the link or the contents.

Which in the end should not be nothing new.

Okay. Linking apparently did not work out right now.

What about an attachment instead while I try solving this problem?

Testing "Lara".

She is supposed to be cute.

By the way, if you did not know it already, she happens to be just a bot.

[IMG]http://i591.photobucket.com/albums/ss355/mittbilde32/r-LARA-LOGAN-large570_zps401097cf.jpg[/IMG]

Anyway, I hear you screaming already.

Tried it out. Linking apparently did not work out.

Oh, another one?

Apparently no tonight.