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2010-06-23, 19:09   #67
Flatlander
I quite division it

"Chris"
Feb 2005
England

31×67 Posts

I'm making a program that calls srsieve then examines the output to give the probabilities of finding a prime by a certain n; as per my question above.

I am using the formulae from your spreadsheet and notice that there is the constant 1.781 in C10. Where does this come from and do I need more significant figures?

You recommend sieving to 1G. Will I lose accuracy by choosing 100M to get a quicker result?

Quote:
 Originally Posted by gd_barnes For the n-value, use a little less than the average of the range; let's say n=140K.
Why 'a little less'?

2010-06-24, 08:14   #68
gd_barnes

"Gary"
May 2007
Overland Park, KS

22·11·269 Posts

Quote:
 Originally Posted by Flatlander I'm making a program that calls srsieve then examines the output to give the probabilities of finding a prime by a certain n; as per my question above. I am using the formulae from your spreadsheet and notice that there is the constant 1.781 in C10. Where does this come from and do I need more significant figures? You recommend sieving to 1G. Will I lose accuracy by choosing 100M to get a quicker result? Why 'a little less'?

AXN came up with the 1.781 constant back about 3 years ago in an RPS thread. Although most are my own, I incorporated a couple of his formulas in the spreadsheet that were over my head to calculate.

Yes, you'll lose a little bit of accuracy with a lower sieve but not a lot. P=1G is pretty fast for one k. You might test the difference.

Think about your 2nd question mathematically. Hint: The chance of prime at each n-level does not drop in a linear fashion. Actually, as n approaches infinity, the % of each n-range that you should use for the "average n" (call it A) would converge on 50, i.e. the true average of the n-range. Technically, the A-value of 40 that I gave was a very rough estimate. 2 examples at the extremes demonstrate this: Let's say you were doing n=1K-1M. The true average is of course near n=500K but A would probably be close to 30, which would mean that you need to use n=300K. For n=10M-11M, A would be very near 50 (likely 45-47 somewhere), which means you would use n=10.5M. The pattern that holds is: If max n / min n divided by the average size of n (call that R) is extremely high as in the former example, than A is very low, possibly as low as 30. If R is extremely low as in the latter example, than A converges on as high as it can be: 50; that is the true average of the n-range.

Actually, I believe it is very possible that the lowest value of A might be the log of 2 base 10, which is .30103. So if max n/min n was very large and the average n was very small, then A would be near 30.103. But I would have to test that to be sure. That is only educated speculation.

I could calculate exact figures across many ranges but it would be tedious and have to be done by trial and error because I don't know enough high-level math to utilize calculus to do it. You would have to take it down to n-ranges that are 1/100th or 1/1000th of your total n-range and add them all together. I only suggest dividing up your sieve ranges into 10, 20, or 30.

What would be more accurate for an n=100K-2M range that you might need to sieve would be to use n=135K for the n=100K-200K range, n=238K for the n=200K-300K range, n=340K for the n=300K-400K range, etc. with the n-range being used gradually converging on 50% of the actual n-range being tested so that it is something like n=1.948M for n=1.9M-2M. But I have no way to know if those are completely accurate. I chose 40% or n=140K (for n=100K-200K) because that is likely to be a reasonably close average over the entire very large n-range that you'd need to sieve just to get a 60-70% chance of prime.

BTW, one final example: Max and I tested Sierp base 9 from n=360K-800K after I sieved n=360K-1M. I remembered commenting to Max, after using the exact method that I showed you to use here that we only had a 20-25% chance of prime for the entire n=360K-1M range. It likely would have needed sieving n=360K-3M to get nearly a 70% chance of prime (If there is no prime by n=1M, it would then probably need sieving n=1M-7M at least!). And the base 9 k is probably about an average-weight k for the 1k conjectures. Imagine what you would need to sieve for a low-weight k. But that one had already been searched to n=360K. For bases at n=100K, I think you'll be able to sieve n=100K-1M for some of them to get a 70% chance of prime, although many will need n=100K-2M I think. Iirc, for the lowest k on Riesel base 3, KEP said he had a 58-60% chance of prime for n=100K-1M, although he did not find one. And that's base 3, which is a far heavier-weight base than all others (although that doesn't necessarily mean the k that he tested is higher than the average k remaining on the 1k bases).

Gary

Last fiddled with by gd_barnes on 2010-06-24 at 08:22

 2010-06-24, 10:03 #69 Flatlander I quite division it     "Chris" Feb 2005 England 207710 Posts Okay, thanks. I'll have to think about some of that. I guessed the sieve files needed to be quiet high to get a >50% probability but I didn't guess that high. I'll continue with the program anyway. It will be interesting to see the stats and maybe a few will be easier to sieve for efficiently than others. Last fiddled with by Flatlander on 2010-06-24 at 10:04
2010-06-25, 06:13   #70
gd_barnes

"Gary"
May 2007
Overland Park, KS

22·11·269 Posts

Quote:
 Originally Posted by Flatlander Okay, thanks. I'll have to think about some of that. I guessed the sieve files needed to be quiet high to get a >50% probability but I didn't guess that high. I'll continue with the program anyway. It will be interesting to see the stats and maybe a few will be easier to sieve for efficiently than others.
I'll clarify on that:

What I was quoting was more like a probability of prime closer to 70%. Honestly I don't know what percentage chance of prime is the best to sieve. Also, the S9 example had already been tested to n=360K, meaning we'd need a much larger n-range to have a 70% chance of prime; hence why I gave the estimated range of n=360K-3M.

But if all you are looking for is a chance of 50% for a single k that is already tested to n=100K, I would guess, on average, you would need to sieve the range of n=100K to n=~1M or 1.5M somewhere. In giving that as a SWAG, I'm using KEP's estimate of 55-60% chance of prime for the lowest remaining Riesel base 3 k for n=100K-1M; which I independently confirmed as close to accurate for that particular k. But base 3 is heavier weight, on average, than all other bases, so I'm assuming that, on average, for other 1k bases, you'll need to sieve a larger range, even to have a 50% chance of prime.

If there any wonder why the final k's are so hard to find a prime for, this example demonstrates why. It's because they are usually one of the lowest weight remaining k's for the base.

Tell you what: You have me curious now. I'll manually calculate these for several 1k bases at n=100K. I'll also give the value of A discussed in the last posting for n=100K-200K, 200K-300K, and 300K-400K as well as n=1.8M-1.9M and 1.9M-2M for future reference. To get a fairly accurate value of A, I'll manually break up each n=100K range into 100 n=1K pieces.

Gary

Last fiddled with by gd_barnes on 2010-06-25 at 06:14

 2010-06-26, 23:26 #71 Flatlander I quite division it     "Chris" Feb 2005 England 31×67 Posts The program is working and producing stats that look about right. At the moment I have average-n fixed at the 40% of range mark and 'partitions' of 25k. This is what I have for S bases 266, 335, 337 and 341 (btw 341 and 337 are out of order in the 1k left thread 1st post.) S266 looks do-able but the rest are pretty depressing! Code: 100000000:P:1:266:257 Estimated probabilities of success for a sieve starting from 25001 : Probability for a sieve to 50008 is :0.3046898 Probability for a sieve to 75008 is :0.4392762 Probability for a sieve to 100008 is :0.5179446 Probability for a sieve to 125006 is :0.5703353 Probability for a sieve to 150006 is :0.6103485 Probability for a sieve to 175026 is :0.6401508 Probability for a sieve to 200054 is :0.663662 Probability for a sieve to 225002 is :0.6832097 Probability for a sieve to 250008 is :0.6996617 Probability for a sieve to 275018 is :0.7137238 Probability for a sieve to 300002 is :0.7264972 Probability for a sieve to 325004 is :0.7375231 Probability for a sieve to 350012 is :0.747241 Probability for a sieve to 375008 is :0.756104 Probability for a sieve to 400002 is :0.7638905 Probability for a sieve to 425030 is :0.7711558 Probability for a sieve to 450056 is :0.7778163 Probability for a sieve to 475004 is :0.7840917 Probability for a sieve to 500028 is :0.7896655 Probability for a sieve to 525014 is :0.7947405 Probability for a sieve to 550008 is :0.7994754 Probability for a sieve to 575006 is :0.8039504 Probability for a sieve to 600006 is :0.8081636 Probability for a sieve to 625004 is :0.812016 Probability for a sieve to 650006 is :0.8159369 Probability for a sieve to 675024 is :0.8195084 Probability for a sieve to 700022 is :0.8228505 Probability for a sieve to 725004 is :0.8259242 Probability for a sieve to 750018 is :0.8288481 Probability for a sieve to 775004 is :0.8316786 Probability for a sieve to 800010 is :0.8344177 Probability for a sieve to 825002 is :0.8369706 Probability for a sieve to 850002 is :0.8393937 Probability for a sieve to 875008 is :0.841714 Probability for a sieve to 900012 is :0.8440081 Probability for a sieve to 925002 is :0.8461736 Probability for a sieve to 950006 is :0.8482533 Probability for a sieve to 975006 is :0.8502517 Probability for a sieve to 999986 is :0.8521671 100000000:P:1:335:257 Estimated probabilities of success for a sieve starting from 25001 : Probability for a sieve to 50010 is :0.1355928 Probability for a sieve to 75042 is :0.2004586 Probability for a sieve to 100002 is :0.2464792 Probability for a sieve to 125006 is :0.2789975 Probability for a sieve to 150018 is :0.3062804 Probability for a sieve to 175002 is :0.3266961 Probability for a sieve to 200046 is :0.345123 Probability for a sieve to 225002 is :0.3605122 Probability for a sieve to 250038 is :0.3740461 Probability for a sieve to 275010 is :0.3856604 Probability for a sieve to 300020 is :0.396175 Probability for a sieve to 325092 is :0.4056267 Probability for a sieve to 350046 is :0.4147946 Probability for a sieve to 375002 is :0.4228382 Probability for a sieve to 400010 is :0.4302676 Probability for a sieve to 425010 is :0.4371182 Probability for a sieve to 450122 is :0.4434187 Probability for a sieve to 475034 is :0.4494008 Probability for a sieve to 500022 is :0.4548441 Probability for a sieve to 525008 is :0.4599947 Probability for a sieve to 550058 is :0.4651467 Probability for a sieve to 575090 is :0.4697821 Probability for a sieve to 600006 is :0.4742179 Probability for a sieve to 625034 is :0.4783694 Probability for a sieve to 650006 is :0.4824371 Probability for a sieve to 675014 is :0.4863998 Probability for a sieve to 700002 is :0.4900967 Probability for a sieve to 725040 is :0.4934128 Probability for a sieve to 750086 is :0.4969392 Probability for a sieve to 775038 is :0.500267 Probability for a sieve to 800042 is :0.5034002 Probability for a sieve to 825038 is :0.5064179 Probability for a sieve to 850026 is :0.5092647 Probability for a sieve to 875016 is :0.5120611 Probability for a sieve to 900054 is :0.5148096 Probability for a sieve to 925058 is :0.5174348 Probability for a sieve to 950066 is :0.5200572 Probability for a sieve to 975006 is :0.5225922 Probability for a sieve to 999962 is :0.5249875 100000000:P:1:337:257 Estimated probabilities of success for a sieve starting from 25001 : Probability for a sieve to 50013 is :0.1454151 Probability for a sieve to 75005 is :0.2250329 Probability for a sieve to 100049 is :0.2736259 Probability for a sieve to 125017 is :0.3094109 Probability for a sieve to 150017 is :0.3368471 Probability for a sieve to 175045 is :0.3600681 Probability for a sieve to 200049 is :0.3794001 Probability for a sieve to 225045 is :0.3961254 Probability for a sieve to 250089 is :0.4104187 Probability for a sieve to 275009 is :0.4235383 Probability for a sieve to 300045 is :0.4347367 Probability for a sieve to 325005 is :0.445013 Probability for a sieve to 350017 is :0.4543006 Probability for a sieve to 375049 is :0.4628028 Probability for a sieve to 400005 is :0.4709361 Probability for a sieve to 425013 is :0.4781026 Probability for a sieve to 450045 is :0.4850882 Probability for a sieve to 475025 is :0.4914963 Probability for a sieve to 500009 is :0.497448 Probability for a sieve to 525077 is :0.5028558 Probability for a sieve to 550009 is :0.508113 Probability for a sieve to 575109 is :0.5131022 Probability for a sieve to 600017 is :0.5178083 Probability for a sieve to 625013 is :0.5222524 Probability for a sieve to 650069 is :0.5265204 Probability for a sieve to 675005 is :0.5304789 Probability for a sieve to 700005 is :0.5342233 Probability for a sieve to 725013 is :0.5380203 Probability for a sieve to 750025 is :0.5416164 Probability for a sieve to 775009 is :0.5451453 Probability for a sieve to 800025 is :0.5483705 Probability for a sieve to 825025 is :0.5515493 Probability for a sieve to 850049 is :0.5546204 Probability for a sieve to 875013 is :0.5575707 Probability for a sieve to 900037 is :0.5604132 Probability for a sieve to 925057 is :0.5631033 Probability for a sieve to 950037 is :0.565847 Probability for a sieve to 975005 is :0.5684015 Probability for a sieve to 999989 is :0.570884 100000000:P:1:341:257 Estimated probabilities of success for a sieve starting from 25001 : Probability for a sieve to 50022 is :0.1208785 Probability for a sieve to 75048 is :0.1858103 Probability for a sieve to 100008 is :0.2279986 Probability for a sieve to 125016 is :0.25898 Probability for a sieve to 150024 is :0.2834809 Probability for a sieve to 175008 is :0.303843 Probability for a sieve to 200010 is :0.3207383 Probability for a sieve to 225036 is :0.3358499 Probability for a sieve to 250044 is :0.3486327 Probability for a sieve to 275004 is :0.3599488 Probability for a sieve to 300006 is :0.3701751 Probability for a sieve to 325032 is :0.3792854 Probability for a sieve to 350016 is :0.3877428 Probability for a sieve to 375054 is :0.3954519 Probability for a sieve to 400110 is :0.4024843 Probability for a sieve to 425034 is :0.4092336 Probability for a sieve to 450030 is :0.4152985 Probability for a sieve to 475020 is :0.4208208 Probability for a sieve to 500070 is :0.4261296 Probability for a sieve to 525006 is :0.431372 Probability for a sieve to 550020 is :0.4361647 Probability for a sieve to 575004 is :0.4405598 Probability for a sieve to 600072 is :0.4447985 Probability for a sieve to 625038 is :0.4490166 Probability for a sieve to 650016 is :0.4527816 Probability for a sieve to 675036 is :0.456551 Probability for a sieve to 700026 is :0.4604775 Probability for a sieve to 725070 is :0.4638947 Probability for a sieve to 750072 is :0.4671016 Probability for a sieve to 775008 is :0.470193 Probability for a sieve to 800004 is :0.4732406 Probability for a sieve to 825030 is :0.4761627 Probability for a sieve to 850056 is :0.479094 Probability for a sieve to 875010 is :0.4817891 Probability for a sieve to 900102 is :0.4844173 Probability for a sieve to 925050 is :0.4869543 Probability for a sieve to 950004 is :0.4895191 Probability for a sieve to 975018 is :0.491972 Probability for a sieve to 999942 is :0.4943631 Do these look about right? When you give me details of the best way to set average-n, I will program it in. (In the meantime I'll probably start adding some code now to work through the S and R lists producing probability files.)
 2010-06-27, 00:35 #72 gd_barnes     "Gary" May 2007 Overland Park, KS 22·11·269 Posts Mark, I'm sorry, I've lost where the posting is now. Can you post a link to the latest version of srfile that can remove many k's at once? It would be very handy for a new effort that I am working on. Thanks, Gary
 2010-06-27, 01:17 #73 kar_bon     Mar 2006 Germany 2,999 Posts The link was in the 33-100 base thread (post #666). Use srsieve V0.6.17 which includes srfile with the new option.
 2010-09-10, 09:08 #74 gd_barnes     "Gary" May 2007 Overland Park, KS 22×11×269 Posts Tim, You had provided a link to all of the needed CRUS software that I put in the 1st posting of this thread. The link does not seem to work now. Can you provide a new link or an attachment to the programs that I can upload to my server machine so that I can provide a link. Gary
 2010-09-10, 09:16 #75 kar_bon     Mar 2006 Germany BB716 Posts Worked for me here! But the ZIP-files contains all older versions! @Gary: If you plan to create such download on the CRUS-page, please include the script-file "new-bases-4.3.txt" and perhaps other tiny scripts/tools, too! Last fiddled with by kar_bon on 2010-09-10 at 09:19
2010-09-10, 09:37   #76
gd_barnes

"Gary"
May 2007
Overland Park, KS

22×11×269 Posts

Quote:
 Originally Posted by kar_bon Worked for me here! But the ZIP-files contains all older versions! @Gary: If you plan to create such download on the CRUS-page, please include the script-file "new-bases-4.3.txt" and perhaps other tiny scripts/tools, too!
Not for me. When I click on the word "here" in:

"Click here to download your attachment" on the google sites page, I get "Internet Explorer cannot display the webpage". I've tried it 4 times. I'm using IE8 in Windows Vista.

If you can post an attachment with the programs, I'll add the starting bases script to it and upload the whole thing to my machine and provide a new link for it.

Gary

 2010-09-10, 10:08 #77 kar_bon     Mar 2006 Germany 56678 Posts I've just uploaded it here and contains (6.0 MB): - LLR / cLLR V3.8.1 - PFGW WIN V3.5 and V3.6 - sr1sieve V1.4.1 - sr2sieve V1.8.11 - srsieve / srfile V0.6.17 - PFGW-script "new-bases-4.3.txt"

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