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General discussion :
Current number of tests for a prime?
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Hello,
it is just a question of interest:
What is the current probability of finding a prime in each subproject?
As I already read there is not an automatically updated list of it.
Does anybody know that?
Thanks in advantage,
MiauiKatze (Austria)  

GellyVolunteer tester
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Joined: 13 Nov 16 Posts: 40 ID: 468732 Credit: 522,960,451 RAC: 0

The only number I know for sure, based on empirical evidence, is that finding or DCing an SGS prime tends to happen after about 15k tasks. The other ones are a lot harder to get good numbers for, since they happen more rarely.  


But is there any list which was recently created or updated?  


But is there any list which was recently created or updated?
I don't know any.
You can always go to Subproject status and look at Range statistics.
For example, for GFN, you'll see https://www.primegrid.com/stats_genefer.php.
That's the current figures for completed WUs and primes found.
I believe that, this way, you can get an idea of how difficult finding a prime is for each subproject.
Edit:
For SGS, in the bottom table line in https://www.primegrid.com/stats_sgs_llr.php you get a total of:
102329878 completed tasks and 8513 primes found.
That's around 12k for each prime found.
____________
"Accidit in puncto, quod non contingit in anno."
Something that does not occur in a year may, perchance, happen in a moment.  


A MILLION thanks to you. I just made a quick look at it, but I think this is exactly what I looked for.
Greeting,
MiauiKatze  


Note that some of the old subprojects may have started with tiny candidates (where it takes relatively few tasks on average to find a prime) and now moved to huge tasks (where finding a prime requires many more tasks). So the numbers may be misleading for 2020; it takes even more tasks than you conclude from these numbers.
However, this is not the case for other subprojects.
/JeppeSN  


True !
Thanks for pointing that out.
____________
"Accidit in puncto, quod non contingit in anno."
Something that does not occur in a year may, perchance, happen in a moment.  

Yves GallotVolunteer developer Project scientist Send message
Joined: 19 Aug 12 Posts: 644 ID: 164101 Credit: 305,010,093 RAC: 0

The number of candidates for one prime is e^{Î³} log(N) / log(p_{max}) where Î³ is Euler's constant and p_{max} is the sieve limit.
For example, if N is a megaprime then N ~ 10^{999999}. For GFN17, p_{max} = 250000Â·10^{15}.
Then 0.5614594836 log(10^999999) / log(250000Â·10^{15}) = 27525.
The probability of finding a prime is 1 / 27525 for GFN17 Mega.  


The number of candidates for one prime is e^{Î³} log(N) / log(p_{max}) where Î³ is Euler's constant and p_{max} is the sieve limit.
For example, if N is a megaprime then N ~ 10^{999999}. For GFN17, p_{max} = 250000Â·10^{15}.
Then 0.5614594836 log(10^999999) / log(250000Â·10^{15}) = 27525.
The probability of finding a prime is 1 / 27525 for GFN17 Mega.
Nice.
If one gets the numbers, just now, from GFN17 Mega in https://www.primegrid.com/stats_genefer.php will calculate 4942404 WUs for 173 found primes, which is ~ 1 / 28.5K
____________
"Accidit in puncto, quod non contingit in anno."
Something that does not occur in a year may, perchance, happen in a moment.  


But is there any list which was recently created or updated?
I don't know any.
You can always go to Subproject status and look at Range statistics.
For example, for GFN, you'll see https://www.primegrid.com/stats_genefer.php.
That's the current figures for completed WUs and primes found.
I believe that, this way, you can get an idea of how difficult finding a prime is for each subproject.
Edit:
For SGS, in the bottom table line in https://www.primegrid.com/stats_sgs_llr.php you get a total of:
102329878 completed tasks and 8513 primes found.
That's around 12k for each prime found.
Strange... The number of GFN17 Mega is not the same in the genefer stat page you mention (https://www.primegrid.com/stats_genefer.php) and in the Primegrid Primes page here (https://www.primegrid.com/primes/primes.php?project=GFN131072).
174 MP in the first one and 172 in the second one.
It seems the error is from the stats_genefer page. The GFN17 LOW is good.
____________
Badge Score: 2*2 + 9*5 + 4*6 + 3*7 + 2*8 + 1*9 = 119  

Ravi FernandoProject administrator Volunteer tester Project scientist Send message
Joined: 21 Mar 19 Posts: 144 ID: 1108183 Credit: 8,505,009 RAC: 0

Strange... The number of GFN17 Mega is not the same in the genefer stat page you mention (https://www.primegrid.com/stats_genefer.php) and in the Primegrid Primes page here (https://www.primegrid.com/primes/primes.php?project=GFN131072).
174 MP in the first one and 172 in the second one.
It seems the error is from the stats_genefer page. The GFN17 LOW is good.
It's not an error. The 173rd and 174th GFN17Megas were discovered today and are currently undergoing further testing.  


I'm running Genefer 15 tasks on an older gpu and it's found 2 prime numbers in the last week, they are not big enough to be in the top 5000 list but they are prime numbers!! I do about 762 tasks per day with my 750Ti gpu with 2gb of ram on it.
Dear Primefinder,
Congratulations! Our records indicate that a computer registered by you has found a unique prime number. This computer is assigned to the Generalized Fermat Prime Search n=15 (GFN15). Since candidates on this subproject are not large enough to report to the Top 5000 Primes List, your prime is visible immediately.
Workunit 683879699 : 202550546^32768+1 (272189 digits)
AND
Dear Primefinder,
Congratulations! Our records indicate that a computer registered by you has found a unique prime number. This computer is assigned to the Generalized Fermat Prime Search n=15 (GFN15). Since candidates on this subproject are not large enough to report to the Top 5000 Primes List, your prime is visible immediately.
Workunit 683182474 : 201919632^32768+1 (272145 digits)
I'm just saying other Projects here still have Prime Numbers to be found in them too..  


Strange... The number of GFN17 Mega is not the same in the genefer stat page you mention (https://www.primegrid.com/stats_genefer.php) and in the Primegrid Primes page here (https://www.primegrid.com/primes/primes.php?project=GFN131072).
174 MP in the first one and 172 in the second one.
It seems the error is from the stats_genefer page. The GFN17 LOW is good.
It's not an error. The 173rd and 174th GFN17Megas were discovered today and are currently undergoing further testing.
Thanks for the info. As they didn't appears on T5K, I though it was a bug.
____________
Badge Score: 2*2 + 9*5 + 4*6 + 3*7 + 2*8 + 1*9 = 119  


This post contains a little bit of everything. Out of curiosity, I did some calculations on the possible amount of missed primes, due to GWNum errors.
During the past 2 years, I have been working mainly on the conjectures Riesel base 383 and Sierpinski base 383, outside of this forum. To aid the development of LLR2, I send 80,807 tests to Stream for the developers to play with. Of those 80,807 tests, 53 had a different residue when LLR2 tests completed, compared to what Prime95 computed as residue.
With these numbers taken into account, I did some calculations, that my overall bad residue production is: 0.06558837724454564579801254841784 % or about 65 in 100,000.
If we generalize this errorrate, we get not only odds for primes but also possible odds for missed primes due to bad residues produced by GWNum. Due to the fact that my computer is at stock settings and vacuumed regularly I think it is a fair assumption to make that we have more or less with old LLR and Prime95 the same overall error rate.
Here we go:
Overall for 14 active projects, we have completed 282,607,863 workunits resulting in 26,047 primes. This gives an overall average odds of finding a prime of: 1 in 10,849.9198756095 tests. Overall, we have potentially 185,357.911307189 bad results being recorded as good results and potentially 17.0838046208868 missed primes overall.
Project Errorpercent Completed tests Primes found Primeodds Possible bad results Possible missed primes
321 Prime Search 0.000655883772445 1,258,351 10 125,835.1 825.3 0.006558837724455
Cullen Prime Search 0.000655883772445 394,408 2 197,204.0 258.7 0.001311767544891
Extended Sierpinski Problem 0.000655883772445 511,556 11 46,505.1 335.5 0.007214721496900
Generalized Cullen Woodall 0.000655883772445 433,067 4 108,266.8 284.0 0.002623535089782
Prime Sierpinski Project 0.000655883772445 380,245 4 95,061.3 249.4 0.002623535089782
Proth Prime Search 0.000655883772445 50,181,192 4743 10,580.1 32,913.0 3.110856732708800
Proth Prime Search Extended 0.000655883772445 144,177,546 16067 8,973.5 94,563.7 10.538084571881200
Proth Prime Search Mega 0.000655883772445 7,084,469 209 33,897.0 4,646.6 0.137079708441101
Fermat Divisor Search 0.000655883772445 2,498,903 44 56,793.3 1,639.0 0.028858885987600
Seventeen Or Bust 0.000655883772445 240,677 1 240,677.0 157.9 0.000655883772445
SR5 0.000655883772445 2,638,343 58 45,488.7 1,730.4 0.038041258801837
SGS 0.000655883772445 70,598,141 4869 14,499.5 46,304.2 3.193498088036930
TRP 0.000655883772445 1,634,107 15 108,940.5 1,071.8 0.009838256586682
Woodall Prime Search 0.000655883772445 576,858 10 57,685.8 378.4 0.006558837724455
So is it worth redoing all those tests with "good results"?  The answer to that question depends on the quality of the work we want to produce. A fortunate thing is that it appears that the conjectures are statistically good and nothing is "missed" due to a residue hiding a prime. However the Proth Prime Search projects does appear to have a possibility of 1314 missed primes. That leaves us with the remaining 12 projects having a possibility of 34 missed primes.
In regards to odds, we can see that the extended Proth Prime Search has the best odds of producing a prime, with odds around 1 in 8,974  while Seventeen Or Bust has the hardest odds, with currently only yielding a prime for 1 in 240,677 tests.
So what can this be used for? Well some can see the odds they have requested others can use this to determine if a rerun of certain tests or ALL pre LLR2 tests is nescessary/worth it, to see if in fact we have missing primes hidden in the pool of composites :)
Take care everyone and sorry if the format of the table is bad, first time I try to make such a table :)
KEP  


Maybe your post should have been in a thread of its own?
This post contains a little bit of everything. Out of curiosity, I did some calculations on the possible amount of missed primes, due to GWNum errors.
During the past 2 years, I have been working mainly on the conjectures Riesel base 383 and Sierpinski base 383, outside of this forum. To aid the development of LLR2, I send 80,807 tests to Stream for the developers to play with. Of those 80,807 tests, 53 had a different residue when LLR2 tests completed, compared to what Prime95 computed as residue.
What is the precise nature of those 53 cases? If LLR2 and Prime95 consistently disagree on a residue (computed in the same manner), it should be possible to determine which of the two programs had the correct one. And then find and fix the bug in the other program.
Out of those 53, which is the smallest candidate number?
/JeppeSN  


Maybe your post should have been in a thread of its own?
Maybe, but at least it answers the question given in the title of this thread.
Out of those 53, which is the smallest candidate number?
/JeppeSN
These are the "guilty" candidates:
434*383^202871+1,C1826C4B544B2438,00CBEA8E7CDBB2E3
434*383^203213+1,1AFF5DB96A7EE147,941C782889FD018A
434*383^203439+1,D763EE33A53C6001,DE647233A2C3B7CB
368*383^205947+1,C0D9EEB67104D2BD,A44E0F2C4854F035
470*383^210019+1,01FD366A3D6B59C2,95810DE00375364B
470*383^210119+1,E96FD79856A2B15B,8ADA7E94EB0F6081
470*383^210299+1,8B44F92A5ECC5303,90FEF4CF1906746A
470*383^210311+1,C3AC0844A0712969,1B0939CE5C4D531C
368*383^213863+1,196EF06E0A16CED3,02510C74DBF7026E
338*383^215011+1,E1D79206BE337F1F,A457588AFD1411AC
338*383^215919+1,79AF23C23DC7E583,60D7A5C4A2DCC1EA
104*383^226971+1,35E745425AF9DCB3,FE19F43D9CAFAA39
118*383^233708+1,761AA7875A422F86,4E396F277C2DA3B8
974*383^261379+1,A20946F65C150876,8E546F16A42B3F13
724*383^263034+1,DB5FC3B804F24E29,FE1AB542FD238AED
716*383^263505+1,85EB6CDD8DF7EAD4,AFE411AB16515755
974*383^264575+1,D24CCD34DAA53383,985530B652FF81C9
970*383^265418+1,C158B3D35D2E88BC,F81BFDF84542262F
974*383^267529+1,2C1CF06DAEED82B5,921EB4978EB44F04
970*383^270576+1,F1FFEF3CA823DD85,54D77DE226534FEF
716*383^276103+1,3F5235A175636793,B62C7BD9FB326DDB
998*383^279335+1,4186247A50168600,16A42B906E66F6AD
716*383^281527+1,F0002F1BD3185A8D,D9F681604A8750B2
902*383^284717+1,B2368F389572D1B6,749DC7EA976D06C9
970*383^286656+1,B35D4C5BFEF98427,21CA934F614E08B5
2*383^290865+1,8E563D05E46B0A11,625AAA1B4B2FFA1C
170*383^2551001,C3FF02ACD2D3DD34,72E46B175ABE00C5
134*383^2786441,3338B1627106632F,8E5BB66742301744
136*383^2840251,1C2B8919E0BED272,68FAC00FA650B5D9
148*383^2937531,6338095D65DEED47,9E7526CEEFDE6D18
170*383^2988781,0421F038F8C606B7,F3601314420BB1B2
170*383^3099521,54298BB7597F126C,306DDD50BFBC54A1
134*383^3125561,FED0CFCE65E70D50,9CF235CCFD880766
170*383^3128341,DEBC0ECD50D1A3D1,DC10C463EA30F479
136*383^3208971,16FB1D21F2E0FECC,10FC2768F11C3713
170*383^3519301,16E9C9BF538CA8AB,566272336F036BE5
134*383^3540641,148CF8B3C9FA11EF,A75D41342482ED46
134*383^3605601,D340C4E745CA3F06,9B222C62799E3F33
134*383^3618881,6CD2E9113D7D186A,4781250BF1D9CFB4
134*383^3652361,0EF29420C1AB5D79,F7ADEA7DF5F97AF4
134*383^3681521,6BA57F9A2E187A35,8AD2B00A7CC6D330
148*383^3693651,70AEB380A37C3CE0,80E3EA82F4B0CC89
134*383^3762401,1A371F111EDFD4D4,6892499F8F2F2F66
178*383^3853371,ECD0777A366A6D87,45F079D9C7B873FF
134*383^3931361,33D2BEEDAF944634,4DD3CB9F724316AB
134*383^3946401,75CE408EBB13A226,4171BBB3801939EB
148*383^4029651,C4F6C667C4D3298A,3CC2619D0A6C2F19
134*383^4044161,22821354006A7860,88B5DE157D28FEBF
134*383^4048961,9852E7C6D811543B,D19B77EC9D94892D
148*383^4053851,A375D6C99AC14EA4,9C3D1D9EBC15BC15
134*383^4083161,73F23A340FAF5552,200667F4B5314C0E
136*383^4100611,98CC1453B7B887CD,DCFC1873DC8BFA15
170*383^4114181,CFA41111C482CA9D,78E83D8FED1E612F
Some of them can be hardware errors, but at least 2 (don't know wich) were reproduceable with the wrong residue and the reason for that wrong residue was due to GWNum selecting a too small FFT.
The first residue is the correct, the last one is mine and not matching LLR2  for unknown reasons, but most likely in more than the 2 cases a wrong FFT selection.
I should add, that I run through P95 and when I have run using LLR, I got some reproducable errors and most of these results are on computers working flawlessly when I enter them in service at PG.
The first 11 I could however expect, due to a dead computer, but if the rest were in fact the result of hardware errors it would be a really really bad thing. One thing that speaks against hardware error, is the relative low count of errors. At least I've seen bad results in the high single figure or low double figure percentages in the past, when I had a computer that was close to dead.  

BurVolunteer tester
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Joined: 25 Feb 20 Posts: 332 ID: 1241833 Credit: 22,611,276 RAC: 0

Due to the doublechecking, hardware errors shouldn't be an issue, I think? Of course, it can still happen that two hardware errors produce the same residue, but that chance is as small as, something something funny and unlikely. So the amount of false negatives in PG projects should be much lower than your prediction?
The first residue is the correct, the last one is mine and not matching LLR2  for unknown reasons, but most likely in more than the 2 cases a wrong FFT selection. So in these two cases the bug was in GWNum? If this is the case for all others isn't that a serious problem? But more importantly for PG, LLR2 apparently did fine?
The number of candidates for one prime is eÎ³ log(N) / log(pmax) where Î³ is Euler's constant and pmax is the sieve limit. Yves, thanks, that's a very useful formula. So far I extrapolated from range stats.
Does anyone have sieve limits for the various PG subprojects? Was it 250,000P for all GFN?
____________
Primes: 1281979 & 12+8+1979 & 1+2+8+1+9+7+9 & 1^2+2^2+8^2+1^2+9^2+7^2+9^2 & 12*8+19*79 & 12^81979 & 1281979 + 4 (cousin prime)  

Yves GallotVolunteer developer Project scientist Send message
Joined: 19 Aug 12 Posts: 644 ID: 164101 Credit: 305,010,093 RAC: 0

Does anyone have sieve limits for the various PG subprojects? Was it 250,000P for all GFN?
For GFN, the sieve limits are http://www.primegrid.com/sieving/gfn/.
I don't know the limits for the other projects.  

Michael GoetzVolunteer moderator Project administrator
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Joined: 21 Jan 10 Posts: 13513 ID: 53948 Credit: 236,960,660 RAC: 2

Please stop with the completely offtopic discussions about LLR errors. It has as little relevance to the question of prime probabilities as does orbital mechanics (or car mechanics), i.e., none at all.
Start a new thread.
This is not a suggestion, folks. We have threads in the forum for a reason. If you don't stay on topic, it's very hard for people to find information.
____________
My lucky number is 75898^{524288}+1  

BurVolunteer tester
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Joined: 25 Feb 20 Posts: 332 ID: 1241833 Credit: 22,611,276 RAC: 0

Yes, sorry. And since I drowned it in my offtopic posting:
Is there a list of the sieving limits for all subprojects? It could be used with Yves' formula to calculate probabilities for prime finding. Maybe it could even be added to the stats page or the preferences? It would go nicely with the average computation times.
____________
Primes: 1281979 & 12+8+1979 & 1+2+8+1+9+7+9 & 1^2+2^2+8^2+1^2+9^2+7^2+9^2 & 12*8+19*79 & 12^81979 & 1281979 + 4 (cousin prime)  

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