20200509, 14:08  #3257 
"James Heinrich"
May 2004
exNorthern Ontario
B76_{16} Posts 
I believe I know the answer, can somebody with knowledge of the source please confirm for me: How does mfaktc handle discovering composite factors?
(I've been using M110393069 for testing which has a thousand composite factors) I believe mfaktc simply returns the composite factor asdiscovered with no attempt to determine if said factor is composite or prime, correct? Assuming thus, a twopart question: a) how practical would it be for mfaktc to detect that a discovered factor is composite? b) if factor is composite, how practical would it be for mfaktc to split the factor into primes? 
20200509, 18:14  #3258  
"TF79LL86GIMPS96gpu17"
Mar 2017
US midwest
2^{3}·3^{2}·59 Posts 
Quote:
With this in mfaktc.ini, Code:
# possible values for StopAfterFactor: # 0: Do not stop the current assignment after a factor was found. # 1: When a factor was found for the current assignment stop after the # current bitlevel. This makes only sense when Stages is enabled. # 2: When a factor was found for the current assignment stop after the # current class. # # Default: StopAfterFactor=1 StopAfterFactor=1 Code:
[Sat May 09 10:09:03 2020] UID: Kriesel/dodortx2080super, M110393069 has a factor: 17743732831822018159 [TF:63:64:mfaktc 0.21 75bit_mul32_gs] [Sat May 09 10:09:03 2020] UID: Kriesel/dodortx2080super, M110393069 has a factor: 13307799624252889361 [TF:63:64:mfaktc 0.21 75bit_mul32_gs] [Sat May 09 10:09:03 2020] UID: Kriesel/dodortx2080super, found 2 factors for M110393069 from 2^63 to 2^64 [mfaktc 0.21 75bit_mul32_gs] There's some question how many factors in one bit level increment mfaktx will find and report. For this remarkable test exponent, more than two factors in a bit level is not an issue until 3 factors at 121122 bits which would take quite a while to run as a test; 4 124125 5 154155 6,7 183184 8+ not found yet Such high bit levels are not supported in mfaktx, although they could be attempted with Factor5 or Ernst's Mfactor and lots of cores and patience. (Mfaktc max 95 bit factors, mfakto max 92 bits) More than one factor per class may be an issue. If so, its overall impact on the GIMPS project is small. See https://www.mersenneforum.org/showpo...82&postcount=5 Although, up to 10 factors / class may be provided for. https://www.mersenneforum.org/showpo...4&postcount=35 Last fiddled with by kriesel on 20200509 at 18:16 

20200509, 18:19  #3259  
"TF79LL86GIMPS96gpu17"
Mar 2017
US midwest
2^{3}×3^{2}×59 Posts 
Quote:
Is the issue of multiple factors in one class closely spaced causing some to be missed still present in mfaktc v0.21? Please suggest some exponent/bitlevel combinations for test of the multiplefactorsperclass case. Last fiddled with by kriesel on 20200509 at 18:23 

20200509, 19:25  #3260  
"James Heinrich"
May 2004
exNorthern Ontario
2·3^{2}·163 Posts 
Quote:
There are three exponents with 11 known factors (thereby 2036 composite factors), and nine exponents with 10 known factors, but of those really only M110393069 is in the "normal" exponent range. https://www.mersenne.ca/manyfactors.php Quote:
Per your example, Factor=110393069,63,64 should ideally return something like: Code:
M110393069 has a composite factor: 13307799624252889361 [TF:63:64:mfaktc 0.21 75bit_mul32_gs] M110393069 has a factor: 1545502967 [TF:63:64:mfaktc 0.21 75bit_mul32_gs] M110393069 has a factor: 8610659383 [TF:63:64:mfaktc 0.21 75bit_mul32_gs] M110393069 has a composite factor: 17743732831822018159 [TF:63:64:mfaktc 0.21 75bit_mul32_gs] M110393069 has a factor: 1545502967 [TF:63:64:mfaktc 0.21 75bit_mul32_gs] M110393069 has a factor: 11480879177 [TF:63:64:mfaktc 0.21 75bit_mul32_gs] found 3 prime factors for M110393069 from 2^63 to 2^64 [mfaktc 0.21 75bit_mul32_gs] Quote:
Code:
100028477 100062071 100071661 100104131 100118399 100250341 100269131 100296149 100297643 100331219 100444901 100475647 100499617 100621361 100683689 100709621 Exponents with three factors sharing a class are rare, these are the only four I found and they're all quite small: Code:
150551 329009 4965187 12671587 

20200509, 20:40  #3261  
"TF79LL86GIMPS96gpu17"
Mar 2017
US midwest
2^{3}×3^{2}×59 Posts 
Quote:
That's what it would take for mfaktc or mfakto to encounter the case where normal use leads to two factors in the same class of the same bit level of the same exponent in the same run, and theoretically finding and reporting two or more factors from that single exponent, bit level, class pass. For an exponent p, p prime, a bit level x1 to x, x <= normal GIMPS factoring depth for p, a class any ONE of 420 or 4620, multiple factors found. Possibly even multiple factors within one block given to one of the many gpu multiprocessors. Instead of at the mfaktc console output, Code:
May 09 10:09  2271 49.5%  0.001 n.a.  1600.63 82485 n.a.% M110393069 has a factor: 17743732831822018159 May 09 10:09  2272 49.6%  0.001 n.a.  1600.63 82485 n.a.% ... May 09 10:09  2860 62.4%  0.001 n.a.  1600.63 82485 n.a.% M110393069 has a factor: 13307799624252889361 May 09 10:09  2872 62.5%  0.001 n.a.  1600.63 82485 n.a.% Code:
May 09 10:09  2271 49.5%  0.001 n.a.  1600.63 82485 n.a.% M110393069 has a factor: 17743732831822018159 M110393069 has a factor: 17743733851853975719 May 09 10:09  2272 49.6%  0.001 n.a.  1600.63 82485 n.a.% I roughly estimated (in the attachment at https://www.mersenneforum.org/showpo...82&postcount=5) that we should find hundreds or thousands of such over the full scope of mersenne.org TF. If we can't identify any coincident class, bit level, exponent multiple factor finds, given how much TF has already been done, we're probably missing some (relatively few) factors this way. Last fiddled with by kriesel on 20200509 at 20:47 

20200509, 21:17  #3262  
"James Heinrich"
May 2004
exNorthern Ontario
2·3^{2}·163 Posts 
Quote:
Code:
106266857 109013999 109088341 109405193 edit: it actually didn't take as long as I feared, here's the complete list of 215 GIMPSrange exponents with samebitsandclass factors: Code:
Factor=630907,49,50 Factor=666493,58,59 Factor=754463,49,50 Factor=976301,49,50 Factor=3902347,37,38 Factor=5279899,42,43 Factor=12953419,49,50 Factor=13904749,45,46 Factor=14298527,54,55 Factor=14749391,68,69 Factor=15162197,41,42 Factor=16892969,62,63 Factor=21474083,40,41 Factor=21633289,51,52 Factor=23740537,55,56 Factor=26936579,39,40 Factor=28247707,56,57 Factor=29235029,60,61 Factor=33838793,61,62 Factor=40917917,47,48 Factor=42416729,59,60 Factor=45632189,45,46 Factor=47916989,60,61 Factor=49678099,65,66 Factor=55346957,62,63 Factor=68168081,62,63 Factor=68989909,52,53 Factor=74542373,65,66 Factor=80374999,54,55 Factor=88079011,45,46 Factor=95469713,66,67 Factor=95669209,63,64 Factor=97267133,46,47 Factor=106266857,63,64 Factor=109013999,53,54 Factor=109088341,53,54 Factor=109405193,54,55 Factor=119525743,49,50 Factor=121156699,51,52 Factor=122522789,57,58 Factor=122617237,53,54 Factor=148380737,50,51 Factor=153225187,64,65 Factor=155676707,54,55 Factor=157910509,60,61 Factor=158599201,57,58 Factor=160739149,64,65 Factor=168830449,50,51 Factor=169014941,59,60 Factor=170473691,59,60 Factor=171953321,64,65 Factor=186375971,45,46 Factor=188904787,54,55 Factor=191462893,61,62 Factor=194559377,59,60 Factor=200995609,48,49 Factor=208394701,58,59 Factor=211943939,65,66 Factor=214423889,62,63 Factor=229769411,48,49 Factor=230055593,63,64 Factor=232507777,62,63 Factor=234028031,43,44 Factor=238430009,65,66 Factor=247462603,50,51 Factor=247575857,61,62 Factor=248693219,61,62 Factor=249720929,58,59 Factor=257601991,53,54 Factor=269222717,59,60 Factor=291566903,51,52 Factor=296611769,63,64 Factor=304843843,50,51 Factor=307436693,63,64 Factor=311095511,64,65 Factor=329514313,51,52 Factor=333341903,57,58 Factor=339049663,45,46 Factor=344226053,50,51 Factor=349871771,44,45 Factor=350800537,49,50 Factor=351511079,59,60 Factor=359812081,48,49 Factor=363424847,47,48 Factor=371542393,49,50 Factor=376397243,45,46 Factor=384190957,46,47 Factor=384327743,56,57 Factor=384394709,55,56 Factor=385356109,53,54 Factor=387013937,60,61 Factor=400835159,51,52 Factor=401102021,52,53 Factor=403918327,54,55 Factor=404784839,61,62 Factor=406884479,53,54 Factor=408071501,44,45 Factor=408188827,69,70 Factor=412778909,60,61 Factor=413747153,54,55 Factor=414824231,60,61 Factor=419128607,57,58 Factor=448196831,55,56 Factor=452020073,43,44 Factor=454609277,63,64 Factor=457729901,62,63 Factor=459228547,54,55 Factor=460167947,47,48 Factor=466220519,57,58 Factor=482584937,63,64 Factor=483370357,59,60 Factor=492464549,64,65 Factor=496423661,55,56 Factor=506824429,48,49 Factor=506895563,62,63 Factor=512880491,57,58 Factor=521816593,53,54 Factor=524087329,46,47 Factor=526005499,49,50 Factor=526014143,58,59 Factor=530664289,46,47 Factor=555551489,67,68 Factor=556353643,48,49 Factor=562335937,54,55 Factor=563680291,55,56 Factor=573868573,47,48 Factor=575599867,46,47 Factor=576806761,57,58 Factor=589429417,55,56 Factor=589746037,46,47 Factor=600953513,59,60 Factor=603618313,60,61 Factor=609388763,48,49 Factor=610146851,63,64 Factor=611741059,63,64 Factor=617863849,48,49 Factor=625400089,54,55 Factor=625521709,61,62 Factor=636713333,56,57 Factor=638366929,60,61 Factor=640381303,50,51 Factor=648452527,62,63 Factor=650749717,53,54 Factor=650927363,54,55 Factor=658195159,50,51 Factor=660280373,60,61 Factor=663891329,53,54 Factor=664600039,61,62 Factor=669290053,57,58 Factor=670620989,49,50 Factor=673902499,53,54 Factor=676343021,64,65 Factor=676611721,43,44 Factor=677065223,54,55 Factor=682014161,64,65 Factor=684732073,59,60 Factor=686029517,63,64 Factor=689997797,44,45 Factor=694678529,45,46 Factor=699891781,54,55 Factor=705410129,61,62 Factor=712472153,47,48 Factor=716225651,48,49 Factor=718763291,43,44 Factor=722281877,48,49 Factor=722671237,63,64 Factor=729992177,57,58 Factor=734571463,52,53 Factor=736663073,57,58 Factor=740774491,47,48 Factor=744550061,60,61 Factor=763981891,64,65 Factor=769814911,49,50 Factor=772482437,52,53 Factor=773120087,48,49 Factor=773476307,46,47 Factor=775692791,44,45 Factor=786451073,61,62 Factor=793651759,54,55 Factor=799473617,45,46 Factor=821119861,52,53 Factor=822585289,48,49 Factor=824575069,46,47 Factor=827289787,49,50 Factor=827753587,69,70 Factor=829322971,53,54 Factor=829364051,62,63 Factor=838613569,48,49 Factor=843158347,48,49 Factor=845831837,57,58 Factor=853745551,47,48 Factor=854811127,58,59 Factor=865444469,50,51 Factor=871148027,53,54 Factor=873514913,58,59 Factor=888502117,56,57 Factor=891816469,51,52 Factor=897478951,45,46 Factor=900842653,63,64 Factor=915151613,65,66 Factor=918760987,57,58 Factor=920280619,49,50 Factor=922496633,58,59 Factor=927602177,54,55 Factor=940010633,50,51 Factor=941381677,52,53 Factor=947056163,54,55 Factor=948726797,63,64 Factor=956418803,47,48 Factor=965694907,62,63 Factor=968105849,44,45 Factor=981595297,50,51 Factor=985010921,51,52 Factor=986248531,45,46 Factor=996709397,46,47 Last fiddled with by James Heinrich on 20200509 at 22:01 

20200509, 22:14  #3263  
"TF79LL86GIMPS96gpu17"
Mar 2017
US midwest
2^{3}·3^{2}·59 Posts 
Quote:
Thanks, while you were getting the big list, I ran the first test case. Console output Code:
May 09 17:02  3607 78.1%  0.216 n.a.  7.70 82485 n.a.% M106266857 has a factor: 15207927026741198039 M106266857 has a factor: 16752154502925095159 May 09 17:02  3615 78.2%  0.217 n.a.  7.66 82485 n.a.% Code:
[Sat May 09 17:02:15 2020] UID: Kriesel/dodortx2080super, M106266857 has a factor: 15207927026741198039 [TF:63:64:mfaktc 0.21 75bit_mul32_gs] UID: Kriesel/dodortx2080super, M106266857 has a factor: 16752154502925095159 [TF:63:64:mfaktc 0.21 75bit_mul32_gs] [Sat May 09 17:02:57 2020] UID: Kriesel/dodortx2080super, found 2 factors for M106266857 from 2^63 to 2^64 [mfaktc 0.21 75bit_mul32_gs] Last fiddled with by kriesel on 20200509 at 22:43 

20200509, 22:17  #3264  
"Seth"
Apr 2019
10011011_{2} Posts 
Quote:
It's really easy to detect if a factor is composite because all factors are of the form (2*k*p+1) so if the factor is composite it must be of the form (2*k_1*p+1)*(2*k_2*p+1) which restricts k_1 and k_2 to be very small so it's easy to just check if the returned factor is divisible by (2*i*p+1) for i <= 1000. I asked about adding this to mfaktc but mfaktc doesn't have good client side big int support so I never coded it up. I think this was asked about in https://www.mersenneforum.org/showpo...postcount=1148 Last fiddled with by SethTro on 20200509 at 22:18 

20200515, 20:14  #3265 
Bemusing Prompter
"Danny"
Dec 2002
California
2,293 Posts 
Silly question: what's the difference between a block and a grid?
I've seen these terms used interchangeably, but my understanding is that they are different things. 
20200518, 19:17  #3266  
"Oliver"
Mar 2005
Germany
3^{3}·41 Posts 
Quote:
Oliver 

20200518, 19:34  #3267  
"TF79LL86GIMPS96gpu17"
Mar 2017
US midwest
2^{3}·3^{2}·59 Posts 
Quote:


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