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Old 2008-06-30, 22:03   #100
gd_barnes
 
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Quote:
Originally Posted by Siemelink View Post
I have already finished this one.

Willem.

Nice work! I'll review it and reflect it on the web pages within the next week or so.

I should preface my prior statement: I hope that no new bases with LARGE conjectures are started in the next few months! It's the large-conjectured bases that take so much time to administer.

The small-conjectured bases like this are kind of fun. I did a few of them myself < 32 before starting the project to knock out some easy stuff.


Gary
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Old 2008-07-02, 06:55   #101
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Gary,

I most certainly agree on having a list of ALL primes, but I tend to disagree (for now at least) for base 3 (or other primes with a huge conjecture).

It will take a LOAD of disc-space, and we won't be near the end of the conjectures anytime soon. When we are, the primes can all be easily generated again (125050976086 as a conjecture with 1/2 eliminated will need 62525488043 entries, with 10 digits for k, and say on average 1 digit for n so a disc space of 687780368473 bytes uncompressed; say it will get compressed 10-fold, you'll need about 68.778.000.000 (68 Gigabyte) storageroom.

Hmm...now that I calculated I think we should save them, even now...
It's not TOO much after all...

(This means I'll have to re-do the range upto 100 to 10k, as I couldn't afford to keep those large files on my laptop...)

What is your opinion on this matter?
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Old 2008-07-02, 18:39   #102
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Quote:
Originally Posted by michaf View Post
Gary,

I most certainly agree on having a list of ALL primes, but I tend to disagree (for now at least) for base 3 (or other primes with a huge conjecture).

It will take a LOAD of disc-space, and we won't be near the end of the conjectures anytime soon. When we are, the primes can all be easily generated again (125050976086 as a conjecture with 1/2 eliminated will need 62525488043 entries, with 10 digits for k, and say on average 1 digit for n so a disc space of 687780368473 bytes uncompressed; say it will get compressed 10-fold, you'll need about 68.778.000.000 (68 Gigabyte) storageroom.

Hmm...now that I calculated I think we should save them, even now...
It's not TOO much after all...

(This means I'll have to re-do the range upto 100 to 10k, as I couldn't afford to keep those large files on my laptop...)

What is your opinion on this matter?

I wondered if you might chime in about base 3. lol Yeah, I'll make an exception there. I personally have all of the primes stored < 30M with the exception of k<10M that I lost when I was laid off from my job. It was stored on my work laptop and I failed to copy it off. I'll rerun it sometime soon. It shouldn't take long.

Here is my opinion: I will trust that you or KEP or whomever runs whatever k-range for base 3 will keep all of the primes that you find. I'm a little surprised that you said you couldn't "afford" (I assume you meant space and not cost) to keep the primes files on your laptop. Each k=1M primes file is just under 8 MB so it shouldn't be a problem with most hard drives >= 60 GB these days. For your k=70M range, that'd only be 550 MB.

As we close in on testing the entire k-range (will WE ever do that, lol?), hopefully there will be a better way to send huge zipped files around the internet and we can deal with it at that point.

Heck, I'm even keeping the RESULTS files for now, 200 MB per k=1M! For the k=20M that I have, that's 4 GB. That's crazy though. My laptop has an 80 GB hard drive so that would fill the entire hard drive in k<400M. I'll probably delete those at some point but the primes definitely need to be kept.

BTW, I run PFGW by k-value instead of n-value on base 3 anyway. It's easiest that way. That way, I don't have to worry about sorting the huge primes files by k. Also, if I have an outage, it's easy to restart PFGW from the k that was left off. If you're processing them by n-range, you can't restart it from the n that was left off. PFGW does not remember the k's that were already eliminated on a restart and it starts searching them all over again. (Yuck!)


Gary

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Old 2008-07-02, 20:13   #103
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Quote:
Originally Posted by gd_barnes View Post
I wondered if you might chime in about base 3. lol Yeah, I'll make an exception there. I personally have all of the primes stored < 30M with the exception of k<10M that I lost when I was laid off from my job. It was stored on my work laptop and I failed to copy it off. I'll rerun it sometime soon. It shouldn't take long.

Here is my opinion: I will trust that you or KEP or whomever runs whatever k-range for base 3 will keep all of the primes that you find. I'm a little surprised that you said you couldn't "afford" (I assume you meant space and not cost) to keep the primes files on your laptop. Each k=1M primes file is just under 8 MB so it shouldn't be a problem with most hard drives >= 60 GB these days. For your k=70M range, that'd only be 550 MB.

As we close in on testing the entire k-range (will WE ever do that, lol?), hopefully there will be a better way to send huge zipped files around the internet and we can deal with it at that point.

Heck, I'm even keeping the RESULTS files for now, 200 MB per k=1M! For the k=20M that I have, that's 4 GB. That's crazy though. My laptop has an 80 GB hard drive so that would fill the entire hard drive in k<400M. I'll probably delete those at some point but the primes definitely need to be kept.

BTW, I run PFGW by k-value instead of n-value on base 3 anyway. It's easiest that way. That way, I don't have to worry about sorting the huge primes files by k. Also, if I have an outage, it's easy to restart PFGW from the k that was left off. If you're processing them by n-range, you can't restart it from the n that was left off. PFGW does not remember the k's that were already eliminated on a restart and it starts searching them all over again. (Yuck!)


Gary
It was indeed a 'space' problem, and not a 'money' problem :)
(Though both are related to eachother ultimately...)

I have kept all the prime > n=10k though (not nearly as much space required for that...

I'll rerun them in the future;
I'll be running upto n=10k with pfgw, k-wise... as in:
first k=2, then k=4, then k=6 etc... with the script I've made for pfgw (I think I posted it somewhere...)
edit: it was here

I'll reserve k=120M to 200M to 10k for sierpinski base 3 now. (as said before, I reckon going to 25k takes too long for a single k)
When we have 500k's left it's time again to go upward to 25k.

What I think of right now too: is there a way to produce a list of all numbers in the range that can be eliminated?

Last fiddled with by michaf on 2008-07-02 at 20:15 Reason: added link
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Old 2008-07-03, 06:11   #104
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Gary, would you be kind and check my reasoning? I think I've got it alright now, but a confirmation would be nice.

Your reasoning is dead on!

One thing I'll mention:
In your (k mod 3^2)=0 list, you state that k=79623216 can be eliminated because it's reduced version has a prime > 2. It does not. If you take it further, it reduces to a k-value that is still remaining, i.e. 79623216/3^3 = 2949008, which just so happens to be the LOWEST k-value remaining and one in which Siemelink tested to n=100K. Regardless, k=79623216 still does not need to be tested so there is no problem that I can see in your final list.

The list will be added to the web pages shortly. Nice work!


Gary
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Old 2008-07-03, 06:25   #105
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Quote:
Originally Posted by michaf View Post
What I think of right now too: is there a way to produce a list of all numbers in the range that can be eliminated?
I'll let you come up with that.

Hint 1:

Take your range of n=120M-200M and divide by 3, then divide by 3^2, then divide by 3^3, etc. and look at the k's remaining on the web page for each of those ranges, i.e. n=40M-66.667M, 13.333M-22.222M, etc.

Hint 2:

Look at the top-10 primes list and multiply each of those by 3, 3^2, 3^3, etc. and see if they fall in your range.

Note to myself: At some point, I should expand this to a top-25 and then a top-50 list for this base. Better yet: I should come up with a list of all primes for n>10K. Base 3 is so huge that I probably should have been keeping many more than 10 primes. The problem is my list of primes for k<10M is gone so I need to rerun it.

Hint 3:

Check the top-5000 site for primes in your k-range. Hint 2 should cover a large # of them.


Suggestion:

Search all even k-values to n=10K. At that point, use the k's found from your elimination list to eliminate k's before starting n=10K-25K. It's far easier to write a PFGW script to just do a step 2 on a huge range then to try to piece-meal out k's to eliminate ahead of time.

One way that I knew that your list of k's to be eliminated was accurate was that they encompossed entire ranges of k-values of k's divisible by 3 that were already remaining with no differences. For example, you had every reduced remaining k from k=16.667M-33.333M in your range of k=50M-100M with no extras and none missing. That's one thing that I was looking for. I mention this because it directly applies to the k-values that you could eliminate before searching n=10K-25K for your new range of k=120M-200M.


Gary

Last fiddled with by gd_barnes on 2008-07-03 at 06:39
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Old 2008-07-03, 11:04   #106
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Quote:
Originally Posted by gd_barnes View Post
Your reasoning is dead on!

One thing I'll mention:
In your (k mod 3^2)=0 list, you state that k=79623216 can be eliminated because it's reduced version has a prime > 2. It does not. If you take it further, it reduces to a k-value that is still remaining, i.e. 79623216/3^3 = 2949008, which just so happens to be the LOWEST k-value remaining and one in which Siemelink tested to n=100K. Regardless, k=79623216 still does not need to be tested so there is no problem that I can see in your final list.

The list will be added to the web pages shortly. Nice work!


Gary
Erm.. yep.. but at least that one SHOULD have a prime above n=2
We just need to determine where...
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Old 2008-07-03, 12:47   #107
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I'm now testing 120-200M for only to n=1k, and am doing about 1M per hour.

1M reduces to about 200 k's.

At this rate, the searchspace will be exhausted in 125050 CPU-hours which is 'only' 14.3 CPU years; after that, some 125050*200 = 62.5M candidates will remain.

(I won't do a complete run through there... I will test all ranges upto 25k first)
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Old 2008-07-03, 20:00   #108
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Stopping the script at n=1k is not a good idea....
srfile takes about 3 minutes to eliminate 1 prime found...
when stopping at 1k, that are LOADS of primes to be eliminated still...
Next run I will try stopping at 5k...
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Old 2008-07-03, 21:50   #109
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Quote:
Originally Posted by michaf View Post
Erm.. yep.. but at least that one SHOULD have a prime above n=2
We just need to determine where...

Ah, good point. lol I should have said it doesn't have a prime above n=2 YET! At least we hope it has one eventually.

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Old 2008-07-03, 21:58   #110
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Quote:
Originally Posted by michaf View Post
Stopping the script at n=1k is not a good idea....
srfile takes about 3 minutes to eliminate 1 prime found...
when stopping at 1k, that are LOADS of primes to be eliminated still...
Next run I will try stopping at 5k...

I think that running PFGW to n=10K on all k's will be the best way to go for large k-ranges. Then use k's remaining to eliminate k's that you can determine can be elminated that already have found primes or are k's remaining for k / 3^q before starting a sieve for n=10K-25K.

I actually used PFGW all the way to n=25K in my efforts because I could just start it and forget it. That's great for a few million k but it sux for MANY million k. It was spending 80% of it's total time or more searching k's for n=10K-25K. In retrospect, it was rather stupid but I was very busy with administering other efforts so I didn't mind just letting 'er rip and forgetting it.


Gary

Last fiddled with by gd_barnes on 2008-07-04 at 01:10
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