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Old 2009-08-13, 10:00   #12
gd_barnes
 
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I do not understand the point in searching ranges randomly. I read all of the points made about doing such and it still doesn't seem like a reasonable method of searching. There is no way to predict when and where primes will occur. Sure, you can even out the # that occur on a daily or whatever basis, but there are easier ways to accomplish that.

Why would you be able to generate any better statistics from such an approach? There is a thread at NPLB where I discuss an exact rating formula for determing if specific k's have a higher density of primes per candidate searched. You do not need to search randomly to come up with such a formula. The formula is: log(continguous search depth)*Nash weight/# primes. We are in the process of computing such a density rating for all k<=1001. It should be the same, regardless of the search depth. The log function guarantees such. In theory, you should get the same density rating for all k's across all n-ranges except Mersenne's but I am speculating that there is a slightly higher density among high-weight k's because I believe the high # of small factors on low weight k's means there will also be a high # of large factors also that would be above most usual sieve depths. We want to break down these ratings by weight classes to prove or disprove such a theory.

If you would like to spread primes out more evenly than the conventional approach taken by NPLB and PrimeGrid, there's a way that is more manageable: Search by k-value broken down by small n-ranges and make those n-ranges random throughout the project. NPLB now searches by k-value (although ordered by n-value within each k) on non-top-5000 ranges because it's much easier for Karsten to list and it does even out the # of primes on about a weekly basis. Here is an example of a suggested approach for your project:

n=650K-775K
n=300K-500K
n=775K-875K
n=70K-300K
n=950K-1M
n=500K-650K
n=875K-950K

NPLB is planning to do k=2000-3000 for n=50K-425K as:
n=50K-250K
n=250K-350K
n=350K-425K
sorted by k-value within each n-range

Sort each file above that I suggested by k-value within each n-range so that if you have more than, say, about 20-40 cores running the project, you'll complete more than one k in a day's time for a given n-range. That way, you're evening out the primes on a somewhat daily (or maybe 3-day or weekly) basis within each n-range.

The idea is that within each n-range, you have a fairly smooth # of primes. Obviously the variance is large from range to range, i.e. you'll have lots of daily primes for n=70K-300K vs. 950K-1M. But for long periods, you'll have similar #'s of primes within each range.

My estimation of the optimum sieve depth for such an effort with the entire file left in the sieve and no n-ranges broken off is about P=60T. If you're sieving n=70K-1M, just LLR an n=721K candidate and sieve until your removal rate equals that testing time. (Note 721K equals 70% of the range from 70K to 1M.)

If you're currently at P=3T after 2 months of sieving, it will take you over 3 years to sieve completely! Even allowing for computer increases in speed and more resources, you're probably still looking at 2 years. Have you considered a DC sieving effort?

If you've already started handing out random n=75K-1M pairs on a server only sieved to P=3T, you are wasting quite a lot of computer resources. You are unlikely to attract many searchers. You made a statement that you thought it didn't make sense to delay the project by months to sieve further. It does if you plan to complete the project! Searching only using a file sieved to 3T would do a grave disservice to the prime searching community. If you plan to only search n=70K-200K at this time, I suppose that you are losing little but you'll still save a little bit of time continuing to sieve that range with the rest of the file.

Managing and testing such an effort will be huge. You've been an admin on a project. You know it takes much more time than expected. Now, try managing a project with 250 times as many k's as the 2 that you had on k=27/121. The computer resources needed to search 500 k's from n=70K to 1M is monsterous...on the order of 100's if not 1000 or more CPU years. Edit: I just noticed on your web page that with the current level of resources, it will take you 25 years to complete the range. Would you like to only take 20 years instead at that level of resources? Yes, sieving from P=3T up to 60T will likely save 20% total time and I'm including sieving time in that.

Even NPLB after nearly 20 months is finally close to completing 50 k's to n=1M. Another 300 k's are at n=710K, 200 more at n=600K (with Benson doing the top-5000 work), and 300 more at n=660K fully filled in up to those limits. But n=700K-1M will take a huge amount of time compared to what we've spent so far. The original project goal was to complete k=300-1001 to n=1M by the end of 2012. I think we will beat that by a year but it still will have taken us 3-4 years and that's only for 350 k's. Also, keep in mind RPS and NPLB have the most favorable k's. It takes less time to test smaller k's. For that reason, NPLB doesn't have much desire to expand above k=3400, the upper limit of our efforts now.

The problem with your approach is that we could not close those ranges until the entire thing was complete. If you adopt something similar to what I suggested, at least we could close ranges of n-values. It would be a little messy for Karsten but I think he could manage it.

One more thing to keep in mind: If it takes you another year to sieve to the optimum depth, the 5000th highest prime is likely to be n>500K. If it takes you even "only" 10-15 years to complete the project, you are risking the 5000th place prime already being at n>1M. When starting a project such as this, it's almost impossible to plan too much. Try to think of everything you can ahead of time. Take a look at the progression of top 5000 primes and see if this fixed n-range over a decade or more is a viable project effort over such a long period. IMHO, it would have been a better idea to pick a small k-range such as k=5000-5200, take more time sieving, and sieve far deeper. Such a project could be completed within the constraints of the rate of increase of the 5000th place prime.

This is just my two cents from experience. Don't take it as being critical of your approach. I hope it will just give you a few more things to consider. Good luck with your project!


Gary

Last fiddled with by gd_barnes on 2009-08-13 at 10:35
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Old 2010-10-19, 23:52   #13
Lennart
 
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I'll post my progress so far on k 5671-5699.

Lennart

kar_bon: updated
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File Type: zip result5671-5699.zip (2.8 KB, 246 views)

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Old 2010-10-27, 10:29   #14
Lennart
 
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Default Status riesel k

k 5671, Primes found 100k-1M:

133915, 271367, 297847

I am continue the search

Lennart

kar_bon: updated

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Old 2010-10-29, 00:11   #15
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Post Riesel k 5699

Riesel k 5699

100k-1M done

5699*2^469724-1 Prime
5699*2^692408-1 Prime

Lennart

kar_bon: updated

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Old 2010-11-02, 19:03   #16
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k 5673, Primes found 100k-500k:

132875, 135484, 167362, 256878, 270883, 360358, 428490, 477792

I am continue the search

Lennart

kar_bon: updated

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Old 2010-11-08, 09:50   #17
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k 5673
5673*2^601034-1Prime
5673*2^700592-1Prime
5673*2^898015-1Prime

Primes found 500k-1M
I am continue the search

Lennart

kar_bon: updated

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Old 2010-11-08, 09:58   #18
Lennart
 
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Default status on k 5715

k=5715, primes for 10k-200k:

12254, 15059, 16070, 28889, 30372, 46126, 49348, 54483, 56310, 62472, 70834, 84110, 84148, 120232, 133454, 142107, 164392, 165800

countinue the search

Lennart

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Old 2010-11-08, 20:41   #19
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K 5675 Status 100k-500k:

123646, 139992, 165290, 194722, 213650, 260032, 291952, 306102, 328632

Lennart

kar_bon: updated

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Old 2010-11-09, 02:19   #20
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K 5677 Status 100k-500k:

115349, 174845, 280297, 380845, 404729

Lennart

kar_bon: updated

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Old 2010-11-09, 23:57   #21
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K 5679 Status 100k-500k:

119965, 148909, 149547, 329151, 340633, 466479

Lennart

kar_bon: updated

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Old 2010-11-10, 14:23   #22
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K 5681 Status 100k-1M <-

194790, 404558, 597570

Lennart

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