The inimitable RDS - Page 3

only_human · 2012-06-06, 18:00

This is soapbox material.

On one had we have a position that work that advances knowledge and approaches the level of curated peer reviewed published mathematics has value.

On the other hand is the feeling that posting pictures of rocks that smashed into houses or owning the cow that knocked over a lantern also has value (and can also advance knowledge).

Well they are both right; or sometimes right and sometimes wrong. And the meaning of value or the purpose of any human endeavor is a contentious terrain strewn with wreckage and tears.

Batalov · 2012-06-06, 18:20

Amen to that!

LaurV · 2012-06-06, 19:07

Opinions vary. If we look not further away than Mersenne primes, one of them was discovered by two highschool students who - at the time of discovery - had very little knowledge about the math behind. They are still "the discoverers". Of course I would want credit if my computer turns out a hundred-megs digit prime. And in spite of the fact that I have not so much idea what my computer is doing the most of the time, I would want the money too

Coming back to our smallest million digits number, one should try first to find the smallest 1k, 2k, 5k, 10k digits number, and then talk about millions. This way, he can get "the sense", and then really appreciate the work other people do.

For 1k digits, pari will spit out a nextprime(10^999) in few seconds, as being 10^999+7. The next one takes longer, the one with the offset 663. Both are proved primes.

But if you want to go to 2k, you will have to sleep in front of the monitor, because behind of 10^1999 is a freaking loooooooong gap. You can use yafu, with "sieverange(10^1999,10^1999+1000,10^8,1)", but still need a couple of trials, as the first 7000 will come empty handed. After about 10-20 minutes the bunch between 7k and 8k stops coming empty, and it will return a "2". You can then play with "testrange(10^1999+7000,10^1999+8000,10^8,20)" for another 20 minutes or so. Both offsets survive and they are 7321 and 7957. You may have to print them in a file to see them. So, the next smallest 5 primes (offset smaller then 20k) with 2000 digits are the one with offsets 12127, 14841, 14967, 16569, and 18027. Quite bigger gaps huh? At this score we expect one prime at each 4603 numbers.

One can try to repeat this "performance" for 5k, then 10k. Try giving to yafu someting like "testrange(10^4999,10^4999+20000,10^8,20)" and if you are still awake when it finishes, dare to move to 9999 zeroes behind.
If it does not come out empty.

Code:

>> testrange(10^4999,10^4999+20000,10^8,20)
ans = 0
>>

Yuck! Nothing, nada, niente. We expect one prime in 11 thousands numbers, at this score of 5k digits. It took about 20 minutes. Wasted. Try higher.

Of course there are faster sievers out there.

But not much faster.

And before talking about millions, there are 10k, 20k, 30k, 50k...

Hundreds of k.

Five hundreds of k.

You don't need to find primes with so many digits, but just to have an idea how much time one would need.

There is quite easy to sieve 10^999999 range. Few lines in pari, not very fast, but working, eliminating almost all numbers. We expect one prime in 2.3M numbers. That is MILLIONS. You have to sieve at least 5-10 millions, to be sure you don't run in a big gap. On this range, there are enough survivors, even if you sieve to 10^10 (which would take a while!)

I wrote a small PRP test routine. I did not like the powermod or modexp functions in yafu/pari/etc because they do not show the progress. It is just classical modular exponentiation, but counting the passed time and computing the remaining time from it. And printing it on the screen. It is comparable as speed (tried for small inputs, up to 10-20 digits modulus) to yafu and much faster than default Mod(x,n)^(n-1) in pari.

I did this because I wanted to know if I have to wait one hour or two or five, for a complete PRP test, assuming I have a sieve-surviving candidate.

Then after about 20 minutes, it says:

Code:

... Done: 0.0013%. ETA: 650:35:32

Batalov · 2012-06-06, 19:26

Every PRP test for KEP will be ~3hours on 1 core. He is prepared to spend 40000 times that. When he will have finished, we could all only congratulate him. That's all there is to it.

If we berate everyone who plays <insert whatever here> instead of running Prime95, we will get an ulcer and at the same time will be ridiculed.

Let's repeat with the late Gregory House: "People don't change!" (That's the second most important lesson after "Everybody lies.")

davieddy · 2012-06-06, 23:43

Quote:

Originally Posted by xilman

Not strictly true.

The value of the computation, IMO, is bragging rights. Look at me, I won the jackpot!

Paul

OK So I'm a bit late to this party.
Meet you in the kitchen.

x

jasong · 2012-06-08, 04:35

I have an idea.

Does anyone know some of the living mathematicians that Mr. Silverman has a great deal of respect for? Maybe if we can convince one of them to tell Silverman to stfu about so-called pointless pursuits, we can move on.

There's plenty of hobbies I don't understand even though I respect the fact that people enjoy them. Nascar, stamp collecting, soccer, over-clocking a gaming machine that's already sufficient for all games being sold. I could go on and on. Why Mr. Silverman continuously flames people that don't give a damn about his opinion expect in that they get offended is beyond me.

This forum doesn't have to be 100% democratic, let's make a rule that incendiary posts that call a project pointless aren't allowed unless they feel the premise for the project is wrong. So you can't make fun of prime-finding projects unless their methodology calls composites primes. If people, for instance, want to start at 1 and find all the prime numbers by brute force from there, that's their own frickin business. Unless somebody brings something new to the table like global warming or setting cats on fire because of an open case, just leave the topic alone.

xilman · 2012-06-08, 06:24

Quote:

Originally Posted by jasong

Does anyone know some of the living mathematicians that Mr. Silverman has a great deal of respect for? Maybe if we can convince one of them to tell Silverman to stfu about so-called pointless pursuits, we can move on.

And what makes you think this hasn't already happened?

I can, but won't, provide names of individuals who have done just that.

Paul

R.D. Silverman · 2012-06-08, 10:01

Quote:

Originally Posted by LaurV

Opinions vary. If we look not further away than Mersenne primes, one of them was discovered by two highschool students who - at the time of discovery - had very little knowledge about the math behind. They are still "the discoverers".

On the contrary. I know Curt. He certainly knew more than "very
little knowledge". He is quite sharp.

AND THEY WROTE THEIR OWN CODE.

retina · 2012-06-08, 10:20

Quote:

Originally Posted by R.D. Silverman

AND THEY WROTE THEIR OWN CODE.

I still don't agree with your argument.

So all those F1 drivers should not get any accolades, it should be the car builders? Oh wait, no, maybe the designers? Oh wait again, it should, of course, be the original inventor of the internal combustion engine, right? Or maybe the oil refining company chemists?

Any code monkey can write code. And it might even work as desired. But so what! I can write code to do FFTs and find MPs, but that doesn't mean I necessarily understand the algorithms I would use. I could just simply follow the steps outlined by someone else in some mathematics paper. Just because I write some code does not instantly make me some hero if someone else runs it and finds something important. There is more to it than that. If someone else chooses to run my code and find important things then full props to them for putting in the effort to both run it and keep it going for long enough to generate results. Many many people out there have no such patience to even run a single number though for testing. Writing code is in some ways the easy part. Investing the time and energy required to run that code for extended periods and sticking with it is also a requirement to achieve success.

R.D. Silverman · 2012-06-08, 11:15

Quote:

Originally Posted by retina

I still don't agree with your argument.

You and others just don't get it. They did their own work.
They did not have it handed to them. It takes almost no intelligence
and effort to run code WRITTEN BY OTHERS.

It also means that they took the time and trouble to learn how
the algorithm works. They might not understand the THEORY and
proof behind the algorithm, but they learned enough to code it.

Quote:

Any code monkey can write code.

Grossly false. I suggest that you try implementing NFS.

R.D. Silverman · 2012-06-08, 12:13

Quote:

Originally Posted by xilman

And what makes you think this hasn't already happened?

I can, but won't, provide names of individuals who have done just that.

Paul

Actually, the mathematicians that I respect are even more contemptuous
of cranks than I am. Indeed, as has been discussed in this forum, they
find the level of discourse here to be so low that they can't even be
bothered with posting herein.

When was the last time you read a post from A. Lenstra, P. Montgomery,
H. Lenstra, C. Pomerance, H. Cohen, H. Williams, R. Brent, S. Wagstaff,
E. Bach, J. Shallit, N. Elkies, J. Buchmann, R. Crandall, Kleinjung, (need I
go on?) etc. in this forum?

They can't be bothered because they know that the participants herein
are, for the most part, WILLFULLY IGNORANT about this subject. They
also know that most of the participants are not going to listen to
any advice they give (in the same way the participants here ignore
[and resent!!] my advice).

I, at least, go to the trouble of telling people when they are wasting their
time. They resent being told this information, but c'est la vie.

When I was a tyro in this subject you can be sure that if Sam Wagstaff
(one of my early mentors) told me that a computation was a waste of time,
that I would take his advice. You could be sure that if he told me that I
should read such and such a book or paper, that I would do so.

I was an ignorant amateur once. But to me, being interested in doing
something meant learning enough so that I could do it myself, and not
have code just handed to me. I started by implementing P-1 after
reading Pollard's paper in detail, and studying the multi-precision arithmetic
algorithms given in Knuth Vol II.

I find it totally contemptuous that people can want credit for blindly
taking code written by others and then trying to claim 'credit' for some
numerical result. This especially applies when they can't be bothered to
learn the math and algorithms.

I have hobbies. I am a amateur at almost all of them (except bridge).

I build model trains, for example. I enjoy watching Norm Abrams on "The
New Yankee Workshop'. But when you have an interest in such things, you
want to build things for yourself. I don't expect 'credit' for (say) buying a
piece of furniture made by someone else. I might expect credit for a piece
of furniture that I built myself, even if it is clear that it was built by
an amateur. but I DO MY OWN WORK.

I will, sometimes, use mathematical software written by others, but only
after I have

(1) learned how it works
(2) coded at least a crude implementation of my own.

For example, I use the CWI post-processing suite. However, I had my
own complete implementation of NFS up and running before CWI wrote their
software. I use their tools because they are more efficient and because I
did not have the time to implement the improved algotithms myself. But
you can be damn sure that I took the time to learn how those algorithms
work.

The cranks herein do NOT do their own work. They take code
written by others that they can be bothered understanding. They
make no effort to learn this subject, but they want 'credit'. It is
pathetic. It is as if they want to be 'amateur carpenters' while not
actually building anything for themselves.

And the suggestiion that I should 'stfu' is totally childish as well.
"Hey everyone! We don't like what the teacher is saying, so let's keep
him from saying it". Suggesting censorship because you don't like
my message is just plain juvenile..////

2012-06-06, 18:00	#23
only_human "Gang aft agley" Sep 2002 2·1,877 Posts	This is soapbox material. On one had we have a position that work that advances knowledge and approaches the level of curated peer reviewed published mathematics has value. On the other hand is the feeling that posting pictures of rocks that smashed into houses or owning the cow that knocked over a lantern also has value (and can also advance knowledge). Well they are both right; or sometimes right and sometimes wrong. And the meaning of value or the purpose of any human endeavor is a contentious terrain strewn with wreckage and tears. Last fiddled with by only_human on 2012-06-06 at 18:04 Reason: s/feeling/feeling that/ added (and can also advance knowledge)

2012-06-06, 19:07	#25
LaurV Romulan Interpreter Jun 2011 Thailand 2⁶·151 Posts	Opinions vary. If we look not further away than Mersenne primes, one of them was discovered by two highschool students who - at the time of discovery - had very little knowledge about the math behind. They are still "the discoverers". Of course I would want credit if my computer turns out a hundred-megs digit prime. And in spite of the fact that I have not so much idea what my computer is doing the most of the time, I would want the money too Coming back to our smallest million digits number, one should try first to find the smallest 1k, 2k, 5k, 10k digits number, and then talk about millions. This way, he can get "the sense", and then really appreciate the work other people do. For 1k digits, pari will spit out a nextprime(10^999) in few seconds, as being 10^999+7. The next one takes longer, the one with the offset 663. Both are proved primes. But if you want to go to 2k, you will have to sleep in front of the monitor, because behind of 10^1999 is a freaking loooooooong gap. You can use yafu, with "sieverange(10^1999,10^1999+1000,10^8,1)", but still need a couple of trials, as the first 7000 will come empty handed. After about 10-20 minutes the bunch between 7k and 8k stops coming empty, and it will return a "2". You can then play with "testrange(10^1999+7000,10^1999+8000,10^8,20)" for another 20 minutes or so. Both offsets survive and they are 7321 and 7957. You may have to print them in a file to see them. So, the next smallest 5 primes (offset smaller then 20k) with 2000 digits are the one with offsets 12127, 14841, 14967, 16569, and 18027. Quite bigger gaps huh? At this score we expect one prime at each 4603 numbers. One can try to repeat this "performance" for 5k, then 10k. Try giving to yafu someting like "testrange(10^4999,10^4999+20000,10^8,20)" and if you are still awake when it finishes, dare to move to 9999 zeroes behind. If it does not come out empty. Code: >> testrange(10^4999,10^4999+20000,10^8,20) ans = 0 >> Yuck! Nothing, nada, niente. We expect one prime in 11 thousands numbers, at this score of 5k digits. It took about 20 minutes. Wasted. Try higher. Of course there are faster sievers out there. But not much faster. And before talking about millions, there are 10k, 20k, 30k, 50k... Hundreds of k. Five hundreds of k. You don't need to find primes with so many digits, but just to have an idea how much time one would need. There is quite easy to sieve 10^999999 range. Few lines in pari, not very fast, but working, eliminating almost all numbers. We expect one prime in 2.3M numbers. That is MILLIONS. You have to sieve at least 5-10 millions, to be sure you don't run in a big gap. On this range, there are enough survivors, even if you sieve to 10^10 (which would take a while!) I wrote a small PRP test routine. I did not like the powermod or modexp functions in yafu/pari/etc because they do not show the progress. It is just classical modular exponentiation, but counting the passed time and computing the remaining time from it. And printing it on the screen. It is comparable as speed (tried for small inputs, up to 10-20 digits modulus) to yafu and much faster than default Mod(x,n)^(n-1) in pari. I did this because I wanted to know if I have to wait one hour or two or five, for a complete PRP test, assuming I have a sieve-surviving candidate. Then after about 20 minutes, it says: Code: ... Done: 0.0013%. ETA: 650:35:32 Last fiddled with by LaurV on 2012-06-06 at 19:23

2012-06-06, 18:20	#24
Batalov "Serge" Mar 2008 Phi(4,2^7658614+1)/2 9,497 Posts	Amen to that!

2012-06-06, 19:26	#26
Batalov "Serge" Mar 2008 Phi(4,2^7658614+1)/2 9,497 Posts	Every PRP test for KEP will be ~3hours on 1 core. He is prepared to spend 40000 times that. When he will have finished, we could all only congratulate him. That's all there is to it. If we berate everyone who plays <insert whatever here> instead of running Prime95, we will get an ulcer and at the same time will be ridiculed. Let's repeat with the late Gregory House: "People don't change!" (That's the second most important lesson after "Everybody lies.")

2012-06-08, 04:35	#28
jasong "Jason Goatcher" Mar 2005 DB3₁₆ Posts	I have an idea. Does anyone know some of the living mathematicians that Mr. Silverman has a great deal of respect for? Maybe if we can convince one of them to tell Silverman to stfu about so-called pointless pursuits, we can move on. There's plenty of hobbies I don't understand even though I respect the fact that people enjoy them. Nascar, stamp collecting, soccer, over-clocking a gaming machine that's already sufficient for all games being sold. I could go on and on. Why Mr. Silverman continuously flames people that don't give a damn about his opinion expect in that they get offended is beyond me. This forum doesn't have to be 100% democratic, let's make a rule that incendiary posts that call a project pointless aren't allowed unless they feel the premise for the project is wrong. So you can't make fun of prime-finding projects unless their methodology calls composites primes. If people, for instance, want to start at 1 and find all the prime numbers by brute force from there, that's their own frickin business. Unless somebody brings something new to the table like global warming or setting cats on fire because of an open case, just leave the topic alone.