is 2 21727 - 1
has 6541 decimal digits
takes 0.000 GHz-days to do one PRP test
Last-known PrimeNet details:
Exponent is not assigned to anyone
-unknown- primality tests remaining
ResidueStatus
L-L-unknown--unknown-
PRP-unknown--unknown-

 Trial FactoringP-1 FactoringCombined
LimitGHz-daysProbabilityB1B2GHz-daysProbabilityGHz-daysProbabilityProb over default TF
Actual2671,367.603377.6119%500000000100000000000.472213.4122%1,368.075580.6147%3.0027%
PrimeNet2400.000062.5000%500100000.00003.7768%0.000063.9163%1.4163%
GPU722440.000165.9091%500100000.00001.5984%0.000166.4540%0.5449%
Difference+23+1,367.6032+11.7028%+499999500+9999990000+0.4722+11.8138%+1,368.0754+14.1607%+14.1607%

Known prime factors (6 factors, 448.4 bits, 2.06389824% known):
Remaining cofactor is not a probable-prime

P-1GHz-days
exponentfactordigitsbits*kdate foundmin B1min B2min. TFmin. P-1normal P-1
217277821721722.899180
22 × 32 × 5
-992.672e-114.176e-98.499e-9
2172729939807824.836689
13 × 53
2008-08-2613531.182e-107.043e-91.228e-8
21727108571049436945911753.269249852831585
3 × 5 × 7 × 2379550777
2008-08-29723795507770.08160.06020.1124
217276301833404019584430690230681275932105.6361450230911773273905898244277
3 × 149 × 9947516393 × 326148188923987
2009-06-0399475163933261481889239875.984e+128,249.415,399
217271810522437127711199143115917899556135113.802416652652719591107640980328140
22 × 5 × 17099491 × 1500074977 × 812171987101
2017-10-1215000749778121719871016.727e+1221.19038.348
2172733596114764065088154877341951194298835139127.9827731420528389811790600943975513025
32 × 52 × 127 × 263489 × 1026858418212615553926623
2021-11-0226348910268584182126155539266238.316e+122.596e+134.848e+13

57 Composite Factors:
exponentprime factorscomposite factordigitsbits*
217272341808171478471547.735
21727849212457372998000111112376.169
217273250596265929619214839372478.105
21727254252570757432871347126119557731101.004
2172749291182674721467952802821814580013823939128.535
21727188675675862499382075070383382878959751340130.471
2172714161401367452998368272891780469233838048142136.701
2172754206692336773307654083455960540555019672742138.638
21727262779436368497945387855357963837422278777207146150.881
217271005861191985959274795013726691760726623218825747152.817
217271475768496082904529263601594183915399944897987347153.370
2172768419666605120742957184111600788389455911808656948158.905
21727423989623791078852717405303239135230549029370716749161.537
2172719657032102809252572620155246173268739345572871055
1
51167.071
2172778675656084416093648089295613532054024040897765730
297
53175.716
2172736475654369386190633013627250359729445920535112147
09441
55181.251
2172753515954309827162272380906657423016236348396791965
65249
55181.804
2172720484716131616602558347015647940654281508345602085
152183
56183.741
2172715375182079621728984156709331225362573718279358256
19678271
58189.971
2172758852774735091317983850093238046515461513975806382
55803657
58191.907
2172728530239176976972438424598155031095336147501381791
828343567961
62204.150
2172710920740520181292560176358282457109801830777585944
0736224617887
63206.087
2172716022573434570434417927657758082602234741373847108
7078617966943
63206.640
2172746032998405373319879195793513198642896214855635827
438822835833697
65214.806
2172711409610773018358300008019264347341486787369039788
85937824919162799
67219.438
2172785418985462252939825075185281418707336285631490308
0654783554443723527
69228.986
2172721171711826546091214566862744700376274429227487070
846578560308675170409
71233.617
2172760826519580657403535856851910176723737237456187520
32331184010208903709911
73241.784
2172789242792185143926500697024448350152201375986953266
35696489864538967357079
73242.337
2172734160154448929045495908819522684138507750687908905
377053492079524803639793
74244.273
2172716559922299964391912089313623434057181360485164939
9269171303316131062566653889
78256.516
2172763387696594640744756852745917181953848379010612199
6141888705979595027737571063
78258.453
2172747576806556093920704188579157971939376674869304850
765077500927515196534788776831
80264.683
2172718211342567266035949846717258182724445852081514253
1428853409347140606756319327177
81266.619
2172726719119741643174266530542774578850253298221838153
1274712217121752826650245343753
81267.172
2172712387534152936868188520373740454561503395039786250
591428063718873440193041664720209
83272.707
2172749580087759593000072031501664808634923689692326466
45784929871223423999950542072459423
85281.352
2172722986349713847080603231523515230621406376966931038
0428528753791536647212284226976557719
87286.887
2172714244404059657866597567101515939023763533458887374
56070222717812125973818644764086211617
88289.518
2172766039990644689133618074551119377304591624777945564
433907268323170600364320768826843791401
89295.053
2172796891836022243513584381766213561993256896553991951
762235305979250483500158042817017859689
89295.606
2172737088038174483831674873960535707766368127733595766
3960992082126773056805710184681766459663
90297.543
2172717979281427014170114298867534107317129730825616080
58115812352635091815769914996111308018414399
94309.786
2172768820687406708682077419539036196636539699495916066
13126728182469125450962877784822331631220233
94311.722
2172751654638166536853489229969605600697024770794977715
8189545592695978271452215408269069446920821121
96317.952
2172719772245741837982355223637721257904596534596681080
55657247869492941402981893504767319533694199607
97319.889
2172729009228703816185037182682947531668606467842454841
15314634949604705480651416271439251034641740023
97320.442
2172753829621592348883948727603428973899215193488089610
86963220548611059039143081138997831258887955208099
3
101334.621
2172715465298973609472518548218686075509879871118208693
80920346446301819912347293904600214331040612864426
3647
104342.788
2172738331859294363815063902576545316165701940760286418
36630270364552190659046402206975046851410193251295
54449
105347.419
2172729982110881177063392544312491860690491034978548824
45504955494609552527386708411674307043365898816771
663754386729
112370.318
2172711476484692244088107969358085694927550961258884086
30608358250725122297590520861212069565471788637764
9110199051343
113372.255
2172789765861323504121079954195495399814418832248800094
42610638505219954302632026421080529973711564095567
1975875234069621303
119395.154
2172741617301904584283304976598134963916068553579404992
76751791720035285730859579172977258980344720043679
395477686603761285359
121400.689
2172732551892427042688499648486214080809655564297165719
94345430108422611514206471846843885908900088400476
8044875126340058324679482839
128423.588
2172712460139868839858573843214876773795990566929365446
58295882310020544879717897445401587492605377115767
92670478609723098357720385713
129425.524
2172797459737675041967444059524509174012349133153323230
21230726877816206317131952524543950324248822899321
42343328621721962609647053059472073
135448.423
P-1 results:
 GHz-DaysworthFactor
probability
dateuseridcompidb1b2estagefactordigitsbits*spentsaved
2016-11-19T00:49:56kkmrkkblmbrbkManual testing5000000001000000000012-
skipped known factor: 7821721
skipped known factor: 29939807
skipped known factor: 10857104943694591
--0.472--13.412%


P+1 Factoring results:
dateuseridcompidb1b2startfactorSmoothdigitsbits*ghz-days
2021-06-28T00:17:06ATHec2-P_11000000001000000000027--0.316


Trial Factoring results:
 BitsFactorGHz-Daysworth
dateuseridcompidfromtofactorbits*digitsspentsaved
2008-08-26T19:59:00ANONYMOUSManual testing??24.83681.53413e-112.11188e-54.65995e-11
2008-08-29T02:24:00ANONYMOUSManual testing??53.269170.0261.43774e-50.055


ECM factoring results:

Old Calculation Method

Total ECM effort:17.899 GHz-days
Estimated T-Level:35.404
DigitsB1CurvesCompleteFacMiss
20110002631 / 10026.3100.000%
25500002631 / 2809.3960.008%
302500002601 / 6404.0641.712%
3510000001692 / 15801.07134.259%
403000000380 / 47000.08192.232%

New Calculation Method

Total ECM effort:17.899 GHz-days
Estimated T-Level:35.404
DigitsB1CompleteFacMiss
2011000340.1460.000%
255000066.6200.000%
3025000010.5370.003%
3510000001.36325.596%
4030000000.14986.184%
45110000000.01498.584%
50440000000.00199.879%


ECM Summary

B1B2factorcurvesGHz-days
10.00000e+0
500005000000300.010
250000250000009091.517
10000001000000009046.036
10000001000000004082.724
30000003000000003236.470
3000000300000000571.142


Lucas-Lehmer results:
No L-L results for M21727


PRP results:
dateuseridcompidcofactorsres64PRP
2017-09-21T19:27:43Oliver KrusePRP
7821721
29939807
10857104943694591
63018334040195844306902306812759
D8A9C29B7907D526no
2017-09-21T20:27:00Oliver KruseManual testing
7821721
29939807
10857104943694591
63018334040195844306902306812759
D8A9C29B7907D526no
2017-10-02T10:24:40kkmrkkblmbrbkManual testing
7821721
29939807
10857104943694591
63018334040195844306902306812759
D8A9C29B7907D5__no
2017-10-13T02:50:43Oliver KruseGTX-34304B5877CBB03__no
2017-10-13T02:57:39Oliver KruseGTX-0AB31ED5F2C972A__no
2017-10-13T03:03:58Oliver KruseGTX-0AB31ED5F2C972A__no
2017-10-13T15:32:09YarBerManual testing
7821721
29939807
10857104943694591
63018334040195844306902306812759
18105224371277111991431159178995561
AB31ED5F2C972A__no
2017-11-01T19:05:55kkmrkkblmbrbkc4.xlarge
7821721
29939807
10857104943694591
63018334040195844306902306812759
18105224371277111991431159178995561
4304B5877CBB03__no
2021-11-02T16:50:40nordisweet16
7821721
29939807
10857104943694591
63018334040195844306902306812759
18105224371277111991431159178995561
335961147640650881548773419511942988351
4304B5877CBB0305no


P-1 factor-bounds graph:
B1 = 500000000, B2 = 10000000000 (P-1 stage 2)
B1 = 500000000 (P-1 stage 1)
100
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102
103
104
105
106
107
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109
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100
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106
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109
1010
1011
1012
1013
1014
1015
1016
1017
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TF factor-bounds graph:
267
2
220
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240
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260
270
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2110
2120
2130
Last modified: 2021-11-03T13:59:17+00:00