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2020-09-08, 21:58
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#34 |
"TF79LL86GIMPS96gpu17"
Mar 2017
US midwest
11001010011002 Posts |
Mprime/prime95 support PRP-CF. No argument there.
Gpuowl DOES NOT support PRP-CF computations. It has never supported the type 5 PRP residues used for PRP-CF. https://www.mersenneforum.org/showpo...3&postcount=15 Supported features and worktodo syntax are often similar or interchangeable, and sometimes differ between GIMPS applications. This is one of the cases where they differ a lot. Putting prime95-like PRP-CF worktodo lines into a gpuowl worktodo file and running whatever gpuowl makes of them doesn't produce PRP-CF computations, as far as I can tell; it produces PRP tests instead. I've confirmed that with a couple short runs. I've looked at several sources and found no evidence to support the claim that gpuowl performs PRP-CF, but numerous indications it does not. Here's how I think gpuowl processes your worktodo line posted previously: PRP=<AID Removed>,1,2,7877777,-1,99,0,3,5,"47266663,9172685364795810287,125872567825872611377" as an assignment in gpuowl worktodo probably parses as follows: PRP=worktype PRP (not PRP-CF) AID=AID echoed in result output 1=k 2=b 7877777=exponent n -1=c 99=TF bits completed 0= number of tests saved if P-1 performed (last of gpuowl supported parameters; gpuowl parser seems to stop after here) 3=base to power; ignored by gpuowl 5= PRP-CF residue type in prime95; ONLY TYPE 1 IS SUPPORTED IN THAT VERSION GPUOWL; gpuowl has only ever implemented 0,1,4 and only one of them at any version; ignored by gpuowl "factor list" ignored by gpuowl, because gpuowl does not support PRP-CF computation. Then it does a PRP test of kbn+c, 1x2787777-1, which is to say, M7877777, with type 1 residue, base 3, the only type and base that version of gpuowl supports. (Which had factors known for years, so it's already known composite.) Gpuowl V6.11-364 and v6.11-380's help.txt and readme.md files do not document a PRP-CF function. From the help.txt: Code:
-prp <exponent> : run a single PRP test and exit, ignoring worktodo.txt -pm1 <exponent> : run a single P-1 test and exit, ignoring worktodo.txt -ll <exponent> : run a single LL test and exit, ignoring worktodo.txt Code:
## worktodo.txt The lines in worktodo.txt must be of one of these forms: * 70100200 * PRP=FCECE568118E4626AB85ED36A9CC8D4F,1,2,77936867,-1,75,0 Looking at the source code, args.cpp contains no parsing for residue type, base, or known factors. In gpu.cpp, occurrences of the string "factor" relate to P-1 factors found. In worktodo.cpp, the relevant code snippet is Code:
if (kind == "PRP" || kind == "PFactor" || kind == "Pfactor" || kind == "DoubleCheck") {
char AIDStr[64] = {0};
if (sscanf(tail, "%32[0-9a-fA-FN/],1,2,%u,-1,%u,%u", AIDStr, &exp, &bitLo, &wantsPm1) == 4
|| sscanf(tail, "%32[0-9a-fA-FN/],%u", AIDStr, &exp) == 2
|| (AIDStr[0]=0, sscanf(tail, "%u", &exp)) == 1) {
string AID = AIDStr;
if (AID == "N/A" || AID == "0") { AID = ""; }
return {{kind == "PRP" ? Task::PRP : (kind == "DoubleCheck" ? Task::LL : Task::PM1), exp, AID, line, B1, B2, bitLo, wantsPm1}};
}
}
But you don't have to take my word for it; Preda, author of gpuowl, has stated gpuowl does not do PRP-CF; 2020-08-06. https://www.mersenneforum.org/showpo...postcount=2391 https://github.com/preda/gpuowl contains no reference to CF or cofactor. When I put up a poll asking about future enhancements, and included PRP-CF in the list of possibilities, no one objected that it was already supported. https://www.mersenneforum.org/showpo...35&postcount=6 How many of the PRP-CF results from you accepted by the PrimeNet server as such were performed on prime95, versus gpuowl, in this list: https://www.mersenne.org/report_prpc...dispdate=1&B1= The status for the exponent corresponding to the worktodo line you gave, https://www.mersenne.org/report_exponent/?exp_lo=7877777&exp_hi=&full=1 shows storm5510 ran a type 1 residue PRP on M7877777 (not type 5 PRP-CF) with offset 0, base 3. NOT a type 5 PRP-CF on M7877777/(product of known factors). For that prime95/mprime is needed. As a confirming experiment, I ran the following worktodo line in gpuowl-win v6.11-340: Code:
PRP=0,1,2,1257787,-1,70,0,3,5,find-me-a-winning-powerball-number Code:
2020-09-08 15:15:24 gpuowl v6.11-340-g41d435f
2020-09-08 15:15:24 config: -device 0 -user kriesel -cpu condorella/rx480 -yield -maxAlloc 7500 -proof 8
2020-09-08 15:15:24 device 0, unique id ''
2020-09-08 15:15:24 condorella/rx480 1257787 FFT: 128K 256:1:256 (9.60 bpw)
2020-09-08 15:15:24 condorella/rx480 Expected maximum carry32: 60000
2020-09-08 15:15:24 condorella/rx480 using long carry kernels
2020-09-08 15:15:27 condorella/rx480 OpenCL args "-DEXP=1257787u -DWIDTH=256u -DSMALL_HEIGHT=256u -DMIDDLE=1u -DPM1=0 -DAMDGPU=1 -DWEIGHT_STEP_MINUS_1=0xa.5644d
df606efp-5 -DIWEIGHT_STEP_MINUS_1=-0xf.a050334c8a45p-6 -cl-unsafe-math-optimizations -cl-std=CL2.0 -cl-finite-math-only "
2020-09-08 15:15:27 condorella/rx480 ASM compilation failed, retrying compilation using NO_ASM
2020-09-08 15:15:32 condorella/rx480 OpenCL compilation in 5.32 s
2020-09-08 15:15:32 condorella/rx480 1257787 OK 0 loaded: blockSize 400, 0000000000000003
2020-09-08 15:15:32 condorella/rx480 1257787 OK 800 0.06%; 172 us/it; ETA 0d 00:04; a0cb6d4276e3bf46 (check 0.07s)
2020-09-08 15:16:02 condorella/rx480 1257787 OK 200000 15.90%; 150 us/it; ETA 0d 00:03; 25ebe34e39ca647b (check 0.06s)
2020-09-08 15:16:32 condorella/rx480 1257787 OK 400000 31.80%; 150 us/it; ETA 0d 00:02; fe2bfeea5734dd7c (check 0.06s)
2020-09-08 15:17:01 condorella/rx480 1257787 OK 600000 47.69%; 145 us/it; ETA 0d 00:02; 0e10714084ddbff9 (check 0.06s)
2020-09-08 15:17:31 condorella/rx480 1257787 OK 800000 63.59%; 148 us/it; ETA 0d 00:01; 27e2b993451c6138 (check 0.07s)
2020-09-08 15:18:01 condorella/rx480 1257787 OK 1000000 79.49%; 148 us/it; ETA 0d 00:01; 4cd95311866a96a2 (check 0.06s)
2020-09-08 15:18:29 condorella/rx480 1257787 OK 1200000 95.39%; 144 us/it; ETA 0d 00:00; 5a5b25f08d9912e4 (check 0.06s)
2020-09-08 15:18:38 condorella/rx480 PP 1257787 / 1257787, 0000000000000001
2020-09-08 15:18:38 condorella/rx480 proof: save residue @ 1257984
2020-09-08 15:18:38 condorella/rx480 1257787 OK 1258000 100.00%; 147 us/it; ETA 0d 00:00; f4d273818ecfa167 (check 0.05s)
2020-09-08 15:18:38 condorella/rx480 {"status":"P", "exponent":"1257787", "worktype":"PRP-3", "res64":"0000000000000001", "residue-type":"1", "errors":{"gerbicz
":"0"}, "fft-length":"131072", "program":{"name":"gpuowl", "version":"v6.11-340-g41d435f"}, "user":"kriesel", "computer":"condorella/rx480", "timestamp":"2020-0
9-08 20:18:38 UTC"}
2020-09-08 15:18:38 condorella/rx480 proof: building level 1, hash fb39419b2846f8a2
2020-09-08 15:18:38 condorella/rx480 proof: building level 2, hash adb074fdf0786521
2020-09-08 15:18:38 condorella/rx480 proof: building level 3, hash e7027375b01a778a
2020-09-08 15:18:39 condorella/rx480 proof: building level 4, hash 02f5a99fbc9b3533
2020-09-08 15:18:39 condorella/rx480 proof: building level 5, hash d7faf41b5ea65ebf
2020-09-08 15:18:39 condorella/rx480 proof: building level 6, hash d4774d2decad9175
2020-09-08 15:18:39 condorella/rx480 proof: building level 7, hash a9b761456b38f66f
2020-09-08 15:18:40 condorella/rx480 proof: building level 8, hash 230b11d9272f1705
 But let's try again, on https://www.mersenne.org/report_expo...1947269&full=1 which has a found factor, and introduce a bogus one also.Code:
PRP=0,1,2,1947269,-1,70,0,3,5,"57431622368499867552481,42" Code:
2020-09-08 15:35:50 gpuowl v6.11-340-g41d435f
2020-09-08 15:35:50 config: -device 0 -user kriesel -cpu condorella/rx480 -yield -maxAlloc 7500 -proof 8
2020-09-08 15:35:50 device 0, unique id ''
2020-09-08 15:35:50 condorella/rx480 1947269 FFT: 128K 256:1:256 (14.86 bpw)
2020-09-08 15:35:50 condorella/rx480 Expected maximum carry32: F60000
2020-09-08 15:35:51 condorella/rx480 OpenCL args "-DEXP=1947269u -DWIDTH=256u -DSMALL_HEIGHT=256u -DMIDDLE=1u -DPM1=0 -DAMDGPU=1 -DWEIGHT_STEP_MINUS_1=0xd.63584
71d0f798p-7 -DIWEIGHT_STEP_MINUS_1=-0xc.1ecf0f7a74f2p-7 -cl-unsafe-math-optimizations -cl-std=CL2.0 -cl-finite-math-only "
2020-09-08 15:35:52 condorella/rx480 ASM compilation failed, retrying compilation using NO_ASM
2020-09-08 15:35:57 condorella/rx480 OpenCL compilation in 5.47 s
2020-09-08 15:35:57 condorella/rx480 1947269 OK 0 loaded: blockSize 400, 0000000000000003
2020-09-08 15:35:57 condorella/rx480 1947269 OK 800 0.04%; 142 us/it; ETA 0d 00:05; ae6256908288407a (check 0.06s)
2020-09-08 15:36:21 condorella/rx480 1947269 OK 200000 10.27%; 120 us/it; ETA 0d 00:03; 07653d81cf4c22c6 (check 0.05s)
2020-09-08 15:36:44 condorella/rx480 1947269 OK 400000 20.54%; 116 us/it; ETA 0d 00:03; 4d9e463546e40492 (check 0.05s)
2020-09-08 15:37:08 condorella/rx480 1947269 OK 600000 30.81%; 119 us/it; ETA 0d 00:03; 2fb23b1c388b7be5 (check 0.05s)
2020-09-08 15:37:32 condorella/rx480 1947269 OK 800000 41.08%; 119 us/it; ETA 0d 00:02; 06b2307e8825791a (check 0.06s)
2020-09-08 15:37:56 condorella/rx480 1947269 OK 1000000 51.35%; 119 us/it; ETA 0d 00:02; fd8187938ddf7c6c (check 0.05s)
2020-09-08 15:38:18 condorella/rx480 1947269 OK 1200000 61.61%; 112 us/it; ETA 0d 00:01; 93aeeb6fb88ad13b (check 0.05s)
2020-09-08 15:38:43 condorella/rx480 1947269 OK 1400000 71.88%; 123 us/it; ETA 0d 00:01; 20294a5c7a5094ae (check 0.05s)
2020-09-08 15:39:07 condorella/rx480 1947269 OK 1600000 82.15%; 121 us/it; ETA 0d 00:01; 8fa7161ac06799b5 (check 0.05s)
2020-09-08 15:39:31 condorella/rx480 1947269 OK 1800000 92.42%; 118 us/it; ETA 0d 00:00; e1e1cd848ecdd6d9 (check 0.05s)
2020-09-08 15:39:48 condorella/rx480 CC 1947269 / 1947269, 5ecc7c3e83061ccb
2020-09-08 15:39:48 condorella/rx480 proof: save residue @ 1947392
2020-09-08 15:39:48 condorella/rx480 1947269 OK 1947600 100.00%; 116 us/it; ETA 0d 00:00; 7088941f68d96ef9 (check 0.05s)
2020-09-08 15:39:48 condorella/rx480 {"status":"C", "exponent":"1947269", "worktype":"PRP-3", "res64":"5ecc7c3e8306____", "residue-type":"1", "errors":{"gerbicz
":"0"}, "fft-length":"131072", "program":{"name":"gpuowl", "version":"v6.11-340-g41d435f"}, "user":"kriesel", "computer":"condorella/rx480", "timestamp":"2020-0
9-08 20:39:48 UTC"}
2020-09-08 15:39:49 condorella/rx480 proof: building level 1, hash 4b254a55ed1d792e
2020-09-08 15:39:49 condorella/rx480 proof: building level 2, hash faeb44f0ad5a2cd8
2020-09-08 15:39:49 condorella/rx480 proof: building level 3, hash a6f14d4f2654d011
2020-09-08 15:39:49 condorella/rx480 proof: building level 4, hash 72e8df2a742892de
2020-09-08 15:39:49 condorella/rx480 proof: building level 5, hash 2df5ac3e964c225d
2020-09-08 15:39:49 condorella/rx480 proof: building level 6, hash a6de185edde216e1
2020-09-08 15:39:50 condorella/rx480 proof: building level 7, hash 9a169bb441adf958
2020-09-08 15:39:51 condorella/rx480 proof: building level 8, hash e38252ffaa1c86ad
2020-09-08 15:39:54 condorella/rx480 PRP-Proof 'C:\msys64\home\ken\gpuowl-compile\gpuowl-v6.11-340-g41d435f\rx480\1947269\1947269-8.proof' generated
To the best of my knowledge, after years of study and tracking developments as they're announced, and reviewing multiple sources relating to the current state of gpuowl including gpuowl source code, PRP-CF is not supported in ANY GIMPS GPU software. If someone else can provide credible information that some gpu package supports PRP-CF, I'd be glad to add it to the tabulation of available software. Last fiddled with by kriesel on 2020-09-08 at 21:59 |
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2020-09-08, 22:59
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#35 | |
"Robert Gerbicz"
Oct 2005
Hungary
156810 Posts |
Quote:
And basically you need only one big division (by mp/d, so there could be a shortcut here because d is "small", a few hundred bits in general) to support prp-cf. That is ((3^mp) mod mp) mod mp/d [so do a fermat test with base=3^d], here we'll use the smallest non-negative residue at mod. And not forget the 2048 bit tricks to save further tests: https://www.mersenneforum.org/showthread.php?t=23462 . |
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2020-09-08, 23:13
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#36 | ||
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"TF79LL86GIMPS96gpu17"
Mar 2017
US midwest
22·1,619 Posts |
Quote:
Quote:
I'm becoming concerned that gpuowl CF capability may be a misunderstanding shared by others also. Last fiddled with by kriesel on 2020-09-08 at 23:23 |
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2020-09-08, 23:24
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#37 | |
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"Robert Gerbicz"
Oct 2005
Hungary
25·72 Posts |
Quote:
(3^mp mod mp) mod 2^2048 (or 3^(1+mp)... ) just as if we'd know only d=1, and then apply my prp cf trick. Ofcourse in this setup we're weaker than a regular Fermat test, but not much weaker because d<<2^2048 so we have a very small chance that we'd identify a composite mp/d as a "probable" prime. And the identified composites here are really composites. ps. not that ideal case, because you need s=3^d mod (mp/d) in the method, so you'd need to compute s with another program with one big division. Last fiddled with by R. Gerbicz on 2020-09-08 at 23:37 |
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2020-09-09, 00:10
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#38 | |
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Random Account
Aug 2009
3·701 Posts |
Quote:
I will ignore the "barbs" above and say that I will not belabor this any longer. I will stick with P-1, while it lasts. Once P-1 is gone, then I do not know what will come after. Perhaps nothing. |
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2020-09-09, 00:29
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#39 | |
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"TF79LL86GIMPS96gpu17"
Mar 2017
US midwest
22×1,619 Posts |
Quote:
I don't change the readme.md that gets put in the zip file of Windows builds. At all. It is the creation of Preda and SELROC. You wouldn't expect CUDALucas to do everything, or disclaim everything else, would you? or CUDAPm1? Or mfaktc? Gpuowl is actually an outlier in doing more than one computation type on gpu in GIMPS. Which one(s) has changed over time and may again. As for "barbs", well, none intended from here, and I suggest you chalk up any you percieve, to word choice or something equally benign. Honestly, trying to help. Last fiddled with by kriesel on 2020-09-09 at 00:30 |
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2020-09-09, 01:35
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#40 | ||
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Einyen
Dec 2003
Denmark
24×32×23 Posts |
Quote:
It was only added to Prime95 around 2 years ago, at least as a feature recorded and handed out by the server. I think you could manually run PRP CF tests for many years if you wanted. I'm not sure how PRP-CF tests works but I believe it is fairly different from a standard PRP test which is "just" 3^(Mp-1) (mod Mp) with modular exponentiation, and since Mp is almost a power of 2 it is mostly just modular squarings. I think some more tricks are needed for PRP-CF tests where you test (2^p-1)/knownfactors which is far from a power of 2, and therefore it should not be expected to be implemented just because PRP tests are working. Also the gpuowl Readme file does not say you can add known factors to the worktodo.txt line: Quote:
Last fiddled with by ATH on 2020-09-09 at 01:38 |
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2020-09-09, 06:45
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#41 | |
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"TF79LL86GIMPS96gpu17"
Mar 2017
US midwest
22·1,619 Posts |
Quote:
One I missed was the gpuowl primenet.py documentation part of readme.md. Code:
## Primenet.py Arguments
-h, --help show this help message and exit\
-u USERNAME Primenet user name\
-p PASSWORD Primenet password\
-t TIMEOUT Seconds to sleep between updates\
--dirs DIR \[DIR ...\] GpuOwl directories to scan\
--tasks NTASKS Number of tasks to fetch ahead\
-w \{PRP,PM1,LL_DC,PRP_DC,PRP_WORLD_RECORD,PRP_100M\} GIMPS work type
Similarly, in the primenet.py code itself: Code:
workTypes = dict(PRP=150, PM1=4, LL_DC=101, PRP_DC=151, PRP_WORLD_RECORD=152, PRP_100M=153) Resorting to a prime95 source code download, we see in primenet.h a list of work preference values Code:
/* Valid work_preference values */ #define PRIMENET_WP_WHATEVER 0 /* Whatever makes most sense */ #define PRIMENET_WP_FACTOR_LMH 1 /* Factor big numbers to low limits */ #define PRIMENET_WP_FACTOR 2 /* Trial factoring */ #define PRIMENET_WP_PMINUS1 3 /* P-1 of small Mersennes --- not supported */ #define PRIMENET_WP_PFACTOR 4 /* P-1 of large Mersennes */ #define PRIMENET_WP_ECM_SMALL 5 /* ECM of small Mersennes looking for first factors */ #define PRIMENET_WP_ECM_FERMAT 6 /* ECM of Fermat numbers */ #define PRIMENET_WP_ECM_CUNNINGHAM 7 /* ECM of Cunningham numbers --- not supported */ #define PRIMENET_WP_ECM_COFACTOR 8 /* ECM of Mersenne cofactors */ #define PRIMENET_WP_LL_FIRST 100 /* LL first time tests */ #define PRIMENET_WP_LL_DBLCHK 101 /* LL double checks */ #define PRIMENET_WP_LL_WORLD_RECORD 102 /* LL test of world record Mersenne */ #define PRIMENET_WP_LL_100M 104 /* LL 100 million digit */ #define PRIMENET_WP_PRP_FIRST 150 /* PRP test of big Mersennes */ #define PRIMENET_WP_PRP_DBLCHK 151 /* PRP double checks */ #define PRIMENET_WP_PRP_WORLD_RECORD 152 /* PRP test of world record Mersennes */ #define PRIMENET_WP_PRP_100M 153 /* PRP test of 100M digit Mersennes */ #define PRIMENET_WP_PRP_COFACTOR 160 /* PRP test of Mersenne cofactors */ #define PRIMENET_WP_PRP_COFACTOR_DBLCHK 161 /* PRP double check of Mersenne cofactors */ Code:
/* This structure is passed for the ga - Get Assignment call */ /* Valid work_types returned by ga */ #define PRIMENET_WORK_TYPE_FACTOR 2 #define PRIMENET_WORK_TYPE_PMINUS1 3 #define PRIMENET_WORK_TYPE_PFACTOR 4 #define PRIMENET_WORK_TYPE_ECM 5 #define PRIMENET_WORK_TYPE_FIRST_LL 100 #define PRIMENET_WORK_TYPE_DBLCHK 101 #define PRIMENET_WORK_TYPE_PRP 150 #define PRIMENET_WORK_TYPE_CERT 200 Code:
/* This structure is passed for the ar - Assignment Result call */ #define PRIMENET_AR_NO_RESULT 0 /* No result, just sending done msg */ #define PRIMENET_AR_TF_FACTOR 1 /* Trial factoring, factor found */ #define PRIMENET_AR_P1_FACTOR 2 /* P-1, factor found */ #define PRIMENET_AR_ECM_FACTOR 3 /* ECM, factor found */ #define PRIMENET_AR_TF_NOFACTOR 4 /* Trial Factoring no factor found */ #define PRIMENET_AR_P1_NOFACTOR 5 /* P-1 Factoring no factor found */ #define PRIMENET_AR_ECM_NOFACTOR 6 /* ECM Factoring no factor found */ #define PRIMENET_AR_LL_RESULT 100 /* LL result, not prime */ #define PRIMENET_AR_LL_PRIME 101 /* LL result, Mersenne prime */ #define PRIMENET_AR_PRP_RESULT 150 /* PRP result, not prime */ #define PRIMENET_AR_PRP_PRIME 151 /* PRP result, probably prime */ #define PRIMENET_AR_CERT 200 /* Certification result */ Code:
// There are (at least) 5 PRP residue types for testing N=(k*b^n+c)/d: #define PRIMENET_PRP_TYPE_FERMAT 1 // Fermat PRP. Calculate a^(N-1) mod N. PRP if result = 1 #define PRIMENET_PRP_TYPE_SPRP 2 // SPRP variant. Calculate a^((N-1)/2) mod N. PRP if result = +/-1 #define PRIMENET_PRP_TYPE_FERMAT_VAR 3 // Type 1 variant,b=2,d=1. Calculate a^(N-c) mod N. PRP if result = a^-(c-1) #define PRIMENET_PRP_TYPE_SPRP_VAR 4 // Type 2 variant,b=2,d=1. Calculate a^((N-c)/2) mod N. PRP if result = +/-a^-((c-1)/2) #define PRIMENET_PRP_TYPE_COFACTOR 5 // Cofactor variant. Calculate a^(N*d-1) mod N*d. PRP if result = a^(d-1) mod N // Primenet encourages programs to return type 1 PRP residues as that has been the standard for prime95, PFGW, LLR for many years. // Primenet encourages programs to return type 5 PRP residues for cofactor tests as that allows Gerbicz-error checking and proofs. CPU Name roa Exponent 10516361 Result type C-PRP received 2020-09-09 04:06 Age days 0.1 Result M10516361/1072668823/249111559369/788796377818991 : F0C2FEF19EB174A1 Ghz-Days 3.4353 The same exponent in Exponent Status shows the known factors, nonzero shift, PRP residue type 5: https://www.mersenne.org/report_expo...0516361&full=1 Last fiddled with by kriesel on 2020-09-09 at 07:07 |
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2020-09-09, 12:58
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#42 | ||
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Random Account
Aug 2009
210310 Posts |
Quote:
Quote:
Having a factor, I don't understand how this could be considered a "first-time" test. The more I think about all of this, the more my head hurts. 
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2020-09-09, 13:46
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#43 | |
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6809 > 6502
"""""""""""""""""""
Aug 2003
101×103 Posts
244348 Posts |
Quote:
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2020-09-09, 13:52
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#44 | |
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"TF79LL86GIMPS96gpu17"
Mar 2017
US midwest
11001010011002 Posts |
Quote:
Another way the situation may occur, is that old factoring gets removed from the database to manage the database size. See the note about that at the bottom of any https://www.mersenne.org/results/ output: Code:
*Count does not include any results reported to the old v4 server. Also, to keep the database size down, some TF-LMH result lines are deleted before 365 days pass. Any factors found, trial factoring limits, and CPU credits are remembered, but the result lines will not appear in the table above or appear in the count of total results for the last 365 days. As to why PRP-CF is called a first-time test, it's the first time the cofactor is primality tested. This is the same terminology and similar sequence as for an exponent with no factor found. The usual order when searching for Mersenne primes is TF up to a stopping point, if no factor found yet, run a P-1, if no factor found yet, then a first primality test, then eventually a double check of the primality test, or now a Cert of the proof. The cofactor being tested for primality in PRP-CF is whatever is left after dividing the Mersenne number by the known factors. See for example https://www.mersenne.org/report_expo...0516361&full=1 (the only PRP-CF I've run.) Or definition of cofactor, #11 of https://www.mersenneforum.org/showpo...65&postcount=3 PRP of a cofactor does not help find new Mersenne primes. It may aid in further factoring of composite Mersenne numbers, which some people like. See https://www.mersenneforum.org/showth...810#post555810 Last fiddled with by kriesel on 2020-09-09 at 13:57 |
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| short runs or long runs | MattcAnderson | Operazione Doppi Mersennes | 3 | 2014-02-16 15:19 |
