20181128, 16:48  #12  
"TF79LL86GIMPS96gpu17"
Mar 2017
US midwest
2×29×59 Posts 
Quote:
In the absence of an answer from someone I think likely to know (which might include heinrich, Prime95, chalsall), I'm leaning toward round down. P1 can pick up the slack based on the roundeddown value of TF limit in its selection of B1 and B2. (And we don't have an app that runs in negative time to un TF exponents that were taken further than optimal. ;) As someone with a variety of cpu types and gpu types, running many of the available computation types on a wide range of exponents (but no Cpu TF, that would be a waste in my fleet), I get the complexity and difficulty of trying to optimize throughput overall. Just measuring and tabulating the GhzD/day values versus exponent, computation type, computationtypespecific variables (TF bit level, B1, B2) versus computing hardware type would be a large undertaking. And some apps compute and display that value, some don't. Then interpreting the data, coming up with a near optimal course for probability of finding a prime (which is not the same as maximizing GhzD/day) seems daunting. Last fiddled with by kriesel on 20181128 at 16:48 

20181128, 17:55  #13  
"/X\(‘‘)/X\"
Jan 2013
Ͳօɾօղէօ
2^{2}·5·139 Posts 
Quote:
When it comes to rounding up or down, down is likely the way to go. Each bit takes roughly twice as long to TF, Personally I TF exponents needing DC, since I want more TF done before my CPUs do the DC. It would probably be faster to do the actual LL work, but I'm lazy and haven't run cudaLucas with a script to manage work fetching and results. The one feature I wish GPU72 had is the ability to tell it which GPU I'm using and for it to only give me "Let GPU72 decide" work based on James' crossovers. This would give the GPUs with the better TF/LL crossover points higher TF work. The difference in crossover for a GTX 580 and a RTX 2080 is several bit levels. 

20181128, 20:33  #14  
"TF79LL86GIMPS96gpu17"
Mar 2017
US midwest
2×29×59 Posts 
Quote:
These are useful as prequalification of those exponents for the P1 application testing I've been doing, exploring the limits of CUDAPm1. See for example https://www.mersenne.org/report_expo...2000100&full=1 Also, running some PRP or LL test & double check well ahead of the wavefront with multiple applications offers a chance of detecting software issues that are fft length or exponent dependent with plenty of time to determine the issue and work on a fix. There's now at least one LLDC in every line through 113M in https://www.mersenne.org/primenet/, which is about 3 years ahead of the leading edge of the mass primality test assignment wave now at ~90M. (PRP coverage is much thinner; no PRP DC above 84M to at least 999M; see https://www.mersenneforum.org/showpo...81&postcount=6) 

20181128, 21:40  #15  
"TF79LL86GIMPS96gpu17"
Mar 2017
US midwest
110101011110_{2} Posts 
Quote:
Quote:
It's hard to even formulate a coherent objective function to consider to optimize, given a very heterogenous pool of computing hardware and computation types that are related and the many constraints. Some may say all gpus should do all TF, all cpus should do no TF. (I think I'd find that approach dull.) I think the lowest TF/LL resources get assigned primality test and P1, and the highest TF/LL resources get assigned TF, until a balance of throughputs of the various types is found, if one is doing all steps on the same exponents. Having the capability of primenet interface and autopilot could help total throughput by gpus. There are probably some users who run prime95 but not gpu apps because they're not automatic. Last fiddled with by kriesel on 20181128 at 21:42 

20181201, 02:19  #16 
"Graham uses ISO 8601"
Mar 2014
AU, Sydney
228_{10} Posts 
Whilst I haven't laboured the Pollard algorithm, my limited grasp for now is that it is not necessarily destined to find results from lapse of reasonable due diligence of TF work; am I wrong?

20181201, 05:35  #17  
Sep 2003
2·1,289 Posts 
Quote:
(Obviously the set of factors of k for a particular factor 2kp+1 of 2^{p}−1 are completely different from the set of factors of 2^{p}−1) So the P−1 algorithm can miss some smallish factors and find some largish factors, whereas TF finds factors strictly on the basis of their size, and there's less overlap than you might think between the factors findable by each method. P−1 won't really bail you out if TF was poorly done with a bad machine. 

20181201, 09:09  #18 
Romulan Interpreter
Jun 2011
Thailand
2^{2}×5×419 Posts 
Well, practical example, if you have your p at the actual front, say in 90M, and you TF to 75 bits and missed a factor, due to bad machine or odd luck, or whatever. There are 2^75/180M, about 2*10^14 factor candidates there. About half of them can not be factors (for example k=2 mod 4). Say you have about 10^13 possible candidates, that you sieve and test. There are about 6 trillion primes there. Any of them can be a factor. I made it in your advantage. In this range, say you make P1 with B1=10M and B2=300M (which is about 10 times higher and longer than the current values we use for this range). About one in a hundred and sixty thousand of these candidates are 10Mpowersmooth and about another one in thirty thousands has the largest prime factor lower than B2. All in all, you may have a chance of 0.0025% plus or minus something, to find a factor by P1 that was missed by TF.
All numbers are from my butt, I didn't use a calculator, and I didn't use advanced tools, just common sense ("feeling" for these numbers, after a lot of experience playing with GIMPS). But that is the ballpark we are in, anyhow. 
20181206, 01:32  #19  
Sep 2003
2×1,289 Posts 
Quote:
I took all the known factors (as of December 1) that meet your conditions: factors of size 75 bits of exponents in the 90M–91M range. There are 125 of them. Slightly more than half of the currentlyknown 75bit factors in this exponent range are findable using P−1 with the B1 and B2 you specified. This is undoubtedly distorted because there has only been very limited TF to 75 bits in this range, so factors found by P−1 are probably overrepresented versus factors found by TF. And also you picked exaggerated values for B1 and B2. But that doesn't matter. Just look at the data. Some of the factors are findable by P−1 using really ridiculously low B1 and B2... and it's a lot more than 0.0025% of them. Whenever you have exponentially increasing difficulty, then you will have a large triviallyeasy group and a large completelyimpossible group, and a small sweet spot in the middle where you can find things with some effort. But the criteria that determine difficulty are different for TF than for P−1, so there will always be some factors that are very hard for TF but are very easy for P−1, and vice versa. We should really choose a bit length like 65 bits, where we can be sure that every factor of this size is known (thanks to complete TF and also user TJAOI), so there is no selection bias. And then I think you'd still find maybe up to 20% of the factors of a given bit length found by TF in a given exponent range are also findable by P−1 with typical values B1 and B2 used by Primenet for that exponent range. The following table shows the fields: p, f, bit length, B1, B2 and the links go to mersenne.ca so you can verify the B1 and B2 values that are needed to find the factor with P−1. Code:
90001337,30275491157952984566993,75,27527,244877 90003091,27580695051547817445769,75,18149,575251 90004207,34105614724956800044441,75,17,61917248641 90011927,24692165690915304167479,75,24907,1835635517 90013493,37379225930359178211089,75,859,30214091639 90016897,37279878084531290742769,75,161743,1367789 90018223,30135935323533343270553,75,67219,419789 90020351,32121394306793985297151,75,431,204419063 90022831,32169364698025037074481,75,3347,190654069 90024941,34710660219198891405431,75,3511,4186691 90026549,22651977832386106845959,75,19867,24517 90034291,23794721359432517352583,75,607,132178369 90034409,30578635633880094849161,75,48023,2130209 90035839,37275245925627483902231,75,59,701702606723 90036091,21970575928536907737983,75,60773,111467 90036179,34807929506691838748903,75,1163,13053311 90040529,31784738502709835530847,75,751,6918347 90041383,23491020791516758138129,75,3,5435237111917 90042629,31629650497580602452961,75,13,6254882089 90043507,28337144191051389713177,75,11383,3455866487 90047663,24097400094846645123049,75,1753,313783 90050803,30975976957801844310913,75,8233,12089423 90052051,28861285992967411012481,75,239,34253 90061571,26211616433883023394961,75,17,23777865599 90061693,36686298667228450938193,75,5897,4220239 90062767,31426249583890764670127,75,263,663378703903 90065617,23085145955421470950559,75,128157374169887,128157374169887 90066673,33770446918217188124401,75,13,1144534253 90070867,34021689523742863765783,75,3,20984519472097 90074161,28662609592468589374529,75,1201,179996759 90074807,27200067254870418199769,75,2129,106165771 90076403,23222441039888242506799,75,43,111028537253 90086989,19616785394967460455521,75,5,1360961333923 90090529,20432166952246868820041,75,4297,101500129 90092983,34383907550131776874927,75,13,1630979139133 90093151,35139954951901562385641,75,23,423956791217 90094969,19558475561072849583463,75,131,39456074549 90095849,20334232711579886881601,75,1129,1372991 90100201,27963683013401722290983,75,1997,4283 90101353,23178295088429391067153,75,3,5359310727283 90102743,25720680603130397485823,75,13,10979210103229 90103477,19344642535218094203617,75,5347,7499 90114347,36353490287781684744673,75,47,8128125443 90115843,36838911275947845397409,75,61,209423697803 90117569,34556576308089107507311,75,349,36624740717 90118949,37409755409195259329287,75,19,3641362364351 90120749,22166173221494404329431,75,7,71708693549 90121459,23714259238860463509703,75,14419,390493 90131891,28496659569941492034839,75,158083111614409,158083111614409 90141127,21039128352619567738673,75,173,84321567977 90141269,34690632245071860114191,75,103,53376892031 90142421,19812699259451178744721,75,30517,4287097 90144179,29813064197700479208209,75,2437,107365889 90149651,22265018841347167697881,75,363437,5663027 90150631,35245101095404158356257,75,48847,83372123 90153013,36137577284545792762591,75,14929,130639 90158807,33343086134850656038961,75,236729,19527929 90162803,26260150014933188168921,75,284387,3657649 90164801,26394575149129829178857,75,139589,23831083 90170033,19782397216081836930073,75,15679,30713 90176059,32279051954330934005257,75,223,66882641167 90188047,29302081806277673160769,75,13,80499817 90189863,21430652709358856941009,75,3,4950356022217 90194723,21607328992446123657959,75,3517,10139291 90197719,34771047234186645032879,75,163,51413453869 90201773,20906787871288193055127,75,617843,5683949 90224671,36966116392160450253041,75,76543,100313 90225743,31311050552132744827639,75,1794719,10742323 90228647,28629910989595726382903,75,372131,38757613 90236819,36736775257229282064913,75,79,1602411757 90240209,26378280401930018845897,75,58897,136319 90243193,20501931601427179977511,75,5,7572845079269 90244949,31348065105309662033249,75,2,10855200710911 90246391,27312496571803352865433,75,7243,1741012261 90248201,23360788510093359122839,75,3,43141743641873 90251617,30478587149629142344903,75,67,44214038537 90255751,30816261664831676831599,75,887,240280727 90258367,26319405133113697433183,75,25603,52201 90261497,19902882946225105086569,75,1237,289376357 90264641,25436083960862831146607,75,17,8288075022599 90265039,19860596701068447730519,75,197,1399598927 90266431,20748280961854176610601,75,6551,125941 90271949,32174383420963682333671,75,17443,681106427 90283153,21071824681658771129983,75,101,7266862333 90287209,19791394593381752283497,75,426739,1088293 90289709,29050985469174247085119,75,71707,190339 90289933,22735974000730158897737,75,153817,1538609 90295097,21850106226467353734433,75,383,2049647 90301931,20313881338512870213263,75,6247,30058517 90302341,31615993367490175356761,75,65761,77339 90303803,37340129698475764263967,75,11981,1462519 90304237,36551719702887556102289,75,3527,98254259 90305447,28444008285058980009367,75,3,17498641942421 90306347,18989540267375199840847,75,585107,5445239 90308021,37206244850926875158431,75,17,89758756837 90308993,25846622933337040303463,75,31,659451830251 90311707,28289617785002206595713,75,443,32203 90323029,23342926586503468755617,75,71,8749941139 90328193,19867594653018597110279,75,109974494081923,109974494081923 90332633,36210287561275510310647,75,639833,11601841 90334411,31159445186129425734511,75,176237,7248959 90347119,29561056405002839372417,75,2,2556204953963 90348067,28406348181925693102831,75,23929,48767 90440143,23991331494887961879943,75,3,4912463667511 90503909,19804045823685690437737,75,953,46218101 90504539,27273508321056276073967,75,1181,29376559 90505357,21224517933807247369991,75,5077,4619089591 90506123,18926107751685058568183,75,433,3135990437 90668371,33743761966549016231081,75,1291,13370963 90673123,27569674045941640318759,75,7069,35801 90679157,29924157598336182932383,75,2927,354539491 90679219,33952994657583975848929,75,3203,1217705149 90682259,29660402175788739276809,75,50131,308809 90682567,36769630201356491264039,75,6091,597263 90684271,28385632387745954602943,75,154753,1011340817 90692821,35742861897608570358569,75,8377,135431 90693371,21212559431297250732497,75,11,1328938427701 90701713,20053913238312793986247,75,3,36849567251857 90719351,34360578429649274048663,75,37,393718171501 90723697,25737172880635507752199,75,2179,7232865097 90724243,26935176168132377274263,75,7,3029496056633 90725827,20912357778960786109847,75,1063,15488550089 90726341,30626793924517436076967,75,3301,396371947 90731723,27760869132060529502767,75,109,514674047 90732647,26075768070729698451583,75,67,714903585953 Last fiddled with by GP2 on 20181206 at 01:48 Reason: fix bad links 

20181206, 01:46  #20 
If I May
"Chris Halsall"
Sep 2002
Barbados
2^{3}·1,103 Posts 
Sigh... Why don't you put your CPUs where your mouth is.
Please run a few P1 jobs in 89M where factors are not known. Many are available. Last fiddled with by chalsall on 20181206 at 01:47 
20181206, 02:01  #21  
Sep 2003
2·1,289 Posts 
Quote:
When a factor of a Mersenne number is known, it's of the form 2kp+1. So you simply find the factors of k itself to determine, retroactively, which B1 and B2 would have sufficed to find that particular factor of the Mersenne number by the P−1 method. Namely, the B1 and B2 values required are the secondlargest and the largest factors of k, respectively. Thus you can determine that a significant fraction of factors found by TF are also findable by P−1. It's demonstrable by math, you don't need to run any jobs to prove it. Last fiddled with by GP2 on 20181206 at 02:03 

20181206, 02:09  #22 
If I May
"Chris Halsall"
Sep 2002
Barbados
2^{3}·1,103 Posts 
You yourself demonstrated that there is little crossover between factors found by TF'ing or P1'ing.
We have now effectively finished TF'ing 89M to 76 bits, and are close to finishing 90M to same. Are you now telling us that we're wasting our time TF'ing? 
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