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

storflyt32 · 2014-10-20, 05:01

In the news:

http://www.fermatsearch.org/news.html

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.

axn · 2014-10-20, 05:11

Factordb says prime

Batalov · 2014-10-20, 05:14

Quote:

Originally Posted by storflyt32

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.

It is a prime number. You just don't know how to use the tools that you claimed to have used.

storflyt32 · 2014-10-20, 05:59

That day again.

Want to know a little more about me?

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

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

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!

storflyt32 · 2014-10-20, 06:36

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.

Batalov · 2014-10-20, 06:53

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.

rajula · 2014-10-20, 06:57

Quote:

Originally Posted by storflyt32

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.

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!

Batalov · 2014-10-20, 07:37

@storflyt32: There's a motto in perl, "there's more than one way to do it". 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, not for primality checks. Using yafu is questionable because this number may be too large for it. (yafu stands for "yet another factoring utility", too.)

With pfgw, however, you can also 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 believe that these tools do 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) -or- 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.")

flagrantflowers · 2014-10-20, 08:12

Quote:

Originally Posted by Batalov

"there's more than one way to do it". 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.

Good post

R.D. Silverman · 2014-10-20, 12:54

Quote:

Originally Posted by Batalov

. 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.")

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

LaurV · 2014-10-20, 15:06

Quote:

Originally Posted by Batalov

Let's have a look...

Very good, instructive, post.

2014-10-20, 05:01	#1
storflyt32 Feb 2013 712₈ Posts	I take a known prime and prove it to be a composite (..or maybe need help?) In the news: http://www.fermatsearch.org/news.html Scroll down towards the bottom (maybe some 5 pages up when using 1024768 resolution). June 23, 2011 New Fermat factor discovered after 1 day! 73332^138560+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. Last fiddled with by storflyt32 on 2014-10-20 at 05:17

2014-10-20, 06:36	#5
storflyt32 Feb 2013 2×229 Posts	Have done a re-check creating a new file with Yafu's ecm command using the number 73332^138560+1. The number starts with 3814 and ends with 009. Still getting a C41715 on this number. Last fiddled with by storflyt32 on 2014-10-20 at 06:40*

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2014-10-20, 05:11	#2
axn Jun 2003 11375₈ Posts	Factordb says prime

2014-10-20, 05:59	#4
storflyt32 Feb 2013 2·229 Posts	That day again. Want to know a little more about me? http://www.primegrid.com/show_user.php?userid=12041 http://www.primegrid.com/show_user.php?userid=170706 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!

2014-10-20, 06:53	#6
Batalov "Serge" Mar 2008 Phi(4,2^7658614+1)/2 3²·17·61 Posts	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.

2014-10-20, 07:37	#8
Batalov "Serge" Mar 2008 Phi(4,2^7658614+1)/2 3²×17×61 Posts	@storflyt32: There's a motto in perl, "there's more than one way to do it". 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"73332^138560+1" > sllr64 -d -q"73332^138560+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, not for primality checks. Using yafu is questionable because this number may be too large for it. (yafu stands for "yet another factoring utility", too.) With pfgw, however, you can also check that this number indeed is a Fermat factor: > pfgw -f1 -gos2 -q"73332^138560+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 believe* that these tools do 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) -or- 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.")