is 2 4211 - 1
has 1268 decimal digits
takes 0.000 GHz-days to do one PRP test
Last-known PrimeNet details:
Exponent is not assigned to anyone
-unknown- L-L tests remaining
ResidueStatus
L-L-unknown--unknown-
PRP-unknown--unknown-

 Trial FactoringP-1 FactoringCombined
LimitGHz-daysProbabilityB1B2GHz-daysProbabilityGHz-daysProbabilityProb over default TF
Actual2677,056.261680.5970%----7,056.261680.5970%13.0970%
PrimeNet2400.000067.5000%500100000.00002.4216%0.000068.2870%0.7870%
GPU722440.000670.4545%500100000.00000.9650%0.000670.7397%0.2851%
Difference+23+7,056.2610+10.1425%-500-100000.0000-0.9650%+7,056.2610+9.8573%+9.8573%

Known prime factors (7 factors, 305.9 bits, 7.26417147% known):
Remaining cofactor is not a probable-prime

P-1GHz-days
exponentfactordigitsbits*kdate foundmin B1min B2min. TFmin. P-1normal P-1
42118423413.0401
1
-112.592e-137.206e-111.466e-10
421192271433826.45910956
22 × 3 × 11 × 83
-11832.912e-91.075e-91.613e-9
421194528529826.49411224
23 × 23 × 61
-23613.035e-91.806e-93.373e-9
42112006147771511237.54623820325
52 × 952813
-259528138.324e-63.742e-66.986e-6
421118981322779671340.788225377853
3 × 75125951
-3751259513.774e-50.00030.0006
42111876665848106411547.41522282900120
23 × 5 × 132 × 3296287
-16932962870.00691.295e-52.417e-5
42112307675252541356382765932017288139135114.1522740056106080926600292011419245
3 × 5 × 15583 × 47487659 × 246851838002138839
-474876592468518380021388394.133e+13969,1061,810,020

120 Composite Factors:
exponentprime factorscomposite factordigitsbits*
42117772022801591239.499
42117962137997671239.534
421116897782679428731650.586
421187222828302120571652.954
4211159879681773160411753.828
421115807156438600291431960.455
4211185110129686984273832064.005
4211189638197797468408792064.040
4211734677882788761561112065.994
42111751433853115694167112167.247
42111794276520836396205432167.282
4211173162647066938787185532373.875
4211177398462046036372770892373.909
42111559182622353468538470092477.045
42111597322540048076407238172477.080
42113807933839474696923320172478.333
421114752327344793491969567532580.287
421115113191135004965238336892580.322
4211376486900904759857484637912684.961
42111458548976244825404463719192786.915
42111494227245813764367849206472786.950
42113562160021249092026714468472788.203
421117498188262309853851283096072890.499
421132074226729895372185125791912891.373
4211165560465775828636430788481192993.741
42113171149166320792279593105115933098.0009
4211163688103049838880856922009853731100.369
4211300040738589811021410159679228131101.243
42111473872397334358989893575181976132103.539
42113513635121375222523554432037036132104.793
42113599583843748652328822814661299332104.828
421113945158032298046046565313770633733106.781
4211347389858522111885709833154418250334111.420
4211355887529302957184262724617299343934111.455
42111378744891988792893457854088997715135113.409
42113286856097359641712538182875602175135114.662
42113367257468712854118709474074859806335114.697
421129595348627343499315898981047955070336117.833
421130319294715894898565674567892124003936117.868
42112926064778331748413333924659664922276938124.460
42112997640659318808363044929451512373669738124.495
42117146219388390880216004140308164659289738125.749
421119437548652155844812037445381617995639339127.192
421127685188908060262144709114361197120867339127.702
421128362409658968370241889900132544148464939127.737
4211332138759466336242199268311891496052896940131.287
421132838252315613350529566648922587051612808742137.914
421160192605908416384059402873815670925197143142138.789
4211212932502450627845201509050815757368660330343140.611
4211218141147032437930527624504908250358270383943140.646
4211310701671918087715053275283563663601403427943141.157
42112797604770984950168044436991062071253550588744144.327
4211276596599254411251510539883874950735734687680146150.955
4211462953756525461857139858908643075904901989704146151.698
4211659391903499210081662051560167414712617381140146152.208
4211675521606695869583834073641240411932441525851346152.243
42111793530468141638340132310735021124316225962116947153.651
42111837402881454224688834181204842192767711443589747153.686
42112617040182566052823893737713456738514621073201747154.197
42114380272883914396796695473720136995095693361209747154.940
4211433073533496469845475656612742451905040308768163149161.567
42113899459491213965222689031587500628346989459277634350164.738
42115554058003173846517839460291290134124376201343062350165.248
42115689918493199309504634402280167989706954972245499950165.283
421120128196232946745333338359153799794080371723913128
7
51167.106
421136895038501210964218565975144713909691025181469303
1
51167.980
421136477783726407655084414556491296723961545207542377
913
53174.607
421142717406527337466545136062918312699273078314548552
9753
54178.157
421143762337599376060401039009901575351325728975901718
2689
54178.192
421162331346672290281681483609104780706516678779005995
9129
54178.702
421116953979687011043594270899915245566553897103052028
30401
55180.146
421140417405592982404176170102477088149379359856740563
25001
55181.399
421141406075233501569111393519172270782487610767021860
15313
55181.434
421139960315530092773083327402273672097211649212800874
0147223
57188.027
421140937804070253521185671124911666634436708073560259
8750799
57188.061
421135980871517976348070968105796094786597713864344246
17109519
58191.197
421136861016959954455675795158040096918421661516402017
29789447
58191.232
421152501693302070104260313643948956789098998535556750
35743567
58191.742
421187874746846705480592965071357566021231330357891411
32795647
58192.485
421134043580730969079037588077316451348222234807332576
425483423
59194.439
421134876337169178371662526761198803680089314549062512
806981399
59194.474
421186880950412390431895290256960726495886996957197271
6301213281
60199.113
421133658573770997142768086670935114007481372131942176
18260059329
61201.067
421134481912368374540894690788513096806186039210359806
89277979977
61201.102
421182203085266287218614563257498989739359910005107046
86891924177
61202.355
421140380136017242089990984241325195466243034623760740
118336823337
62204.651
421174016899268980026303454479604477859683149560451935
761537734681
62205.525
421138205978967009993896568166409383989641631502193361
7865490453529
63207.893
421173179824532356460785402983438019927485617537047261
89405119465863
64212.153
421137773898454355250730977337623214787777622017500745
905260233624967
65214.521
421169239658719793724239046631791399057462852197301665
577690677342871
65215.395
421134012188567323012399406026468212141216508063593671
4016751062967551
66217.691
421181083288160577460232665768531098721711232766190433
8162297644852151
66218.945
421183066705556664575766910359438107490073804274445186
5456566168513263
66218.980
421132180896083912517859079366566624134475146214297468
63281026090074767
67220.933
421180166297949532061064673379607044584965618153072319
170015409076501673
68225.572
421182127284406052109007364700185294864275223725913340
500088012368193649
68225.607
421131816954668103427690702211480033815745091025340878
2760006947823097041
69227.561
421175849964745415082511500264385797793030353989222645
3299334159939135641
69228.814
421177705367294837040671360827088277190477856943551516
2805299174431345633
69228.849
421168296453617654394753974376833744453297371358962202
40341033062589667873
70231.985
421169967086090378572168468595754717938889165340365180
62740656837387214249
70232.020
421167524072762890855034774387643013653916540170332814
4369039790651373591679
72238.612
421169175811655217691416903286966073864179020944336806
7032241328177295105527
72238.647
421116491153631820861855520226866352456169323919057965
47950794599590444079727
73239.901
421163888425305063123999436672692157481069467165122234
16140291629167339504143
73241.854
421165451230872441239357487224656455877539498903553442
16309034946235224266759
73241.889
421176646839563025031063498928478992529171431961645826
425200559628038256515879
74245.439
421175780022205449819707817484397125226542153995856231
61760057527334951614729017
76252.066
421113890498704082711940904687089528673831421537022524
323389542912350310483540521
77252.941
421171699855920859472442257455755005538666058149504985
165273254818497221675202089
77255.309
421164559632963935983664785147457855407321097141294279
5979464313746966234633248817
78258.479
421163829512703650383139894667107698578316456310709703
891504964552742297450862510191
80265.107
421115216623774312653227038902934434406138132086526544
8485873031192871488342776538791
81266.360
421115588844943290336627145375754225772772231649930645
4251066577880428681313352031583
81266.395
421160392788642139933638113454982441165218420779328049
0047096625336202098170227195647
81268.349
421112816962205103547813134867941674100290148656481308
72596508541737556546311206786236593
85279.400
421113130484095733450541044549997784368406050718736582
64156733785486850782702364162023609
85279.435
421114384050617322030956390905201658678592261969470550
039894854919433257079083313987624668439
89292.854
421112115685834970346674568059451357104978262256885044
2986034362986386324377118753717762582261697
93305.894
P-1 results:
Exponent "4211" not found


Trial Factoring results:
 BitsFactorGHz-Daysworth
dateuseridcompidfromtofactorbits*digitsspentsaved
2009-10-25T00:00:00Carsten Kossendeyv4_computers??113.409351.11687e+134.91851e-72.62507e+13


ECM factoring results:
Total ECM effort:23.696 GHz-days
Estimated T-Level:39.629
DigitsB1CurvesCompleteFacMiss
20110004441 / 10044.4100.000%
25500004441 / 28015.8610.000%
302500004441 / 6406.9390.096%
3510000004351 / 15802.7546.363%
4030000004351 / 47000.92639.620%
4511000000828 / 97000.08591.818%

ECM Summary

B1B2factorcurvesGHz-days
30000003000000003,52310.96
1100000011000000900.696
1100000011000000001281.460
11000000220000000070010.58


Lucas-Lehmer results:
Exponent "4211" not found


PRP results:
dateuseridcompidcofactorsres64PRP
2017-09-21T18:33:45Oliver KruseOliver-PCF7A841A91CEE8C__?
2017-09-21T19:21:10Oliver KruseManual testingF7A841A91CEE8C__?
2017-10-02T09:55:57kkmrkkblmbrbkManual testing
8423
92271433
94528529
200614777151
1898132277967
187666584810641
23076752525413563827659320172881391
F7A841A91CEE8C__no
2017-12-07T02:44:27ATHManual testing
8423
92271433
94528529
200614777151
1898132277967
187666584810641
23076752525413563827659320172881391
F7A841A91CEE8C__no
2020-04-17T12:32:19Oliver KruseIOS-1
8423
92271433
94528529
200614777151
1898132277967
187666584810641
23076752525413563827659320172881391
1CD5FB0B28CFC3__no


P-1 factor-bounds graph:
100
101
102
103
104
105
106
107
108
100
101
102
103
104
105
106
107
108
109
1010
1011
1012
1013
1014
1015
1016
1017
1018
TF factor-bounds graph:
267
2
210
220
230
240
250
260
270
280
290
2100
2110
2120
Last modified: 2020-04-17T12:32:19+00:00