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
0 primality tests remaining
ResidueStatus
L-L-unknown--unknown-
PRP-unknown--unknown-

 Trial FactoringP-1 FactoringCombined
LimitGHz-daysProbabilityB1B2GHz-daysProbabilityGHz-daysProbability
Actual2677,056.261680.5970 %770000000007747412066312618703,041,531.620441.4003 %3,048,587.882088.6299 %
Target2440.000670.4545 %500500000.00000.9650 %0.000670.7397 %
Difference+23+7,056.2610+10.1425 %+76999999500+774741206631211870+3,041,531.6204+40.4353%+3,048,587.8814+17.8902 %

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
2009-10-25112.592e-137.206e-111.466e-10
421192271433826.45910956
22 × 3 × 11 × 83
2009-10-2511832.912e-91.075e-91.613e-9
421194528529826.49411224
23 × 23 × 61
2009-10-2523613.035e-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
2009-10-2516932962870.00691.295e-52.417e-5
42112307675252541356382765932017288139135114.1522740056106080926600292011419245
3 × 5 × 15583 × 47487659 × 246851838002138839
-474876592468518380021388394.133e+13969,1061,810,020

120 Composite Factors:
P-1 results:
dateusercompB1B2BSstagefactordigitsbits*GHz-daysFac Prob
2009-10-25Carsten Kossendeyv4_computers35113.409-0.000%
2021-08-27Seth_TrManual testing100000000100000000
skipped known factor: 8423
skipped known factor: 92271433
skipped known factor: 94528529
skipped known factor: 200614777151
skipped known factor: 1898132277967
skipped known factor: 187666584810641
--0.00725.202%
2023-05-18ANONYMOUSGreatLakes77000000000774741206631261870
skipped known factor: 8423
skipped known factor: 92271433
skipped known factor: 94528529
skipped known factor: 200614777151
skipped known factor: 1898132277967
skipped known factor: 187666584810641
skipped known factor: 23076752525413563827659320172881391
--3,878,00080.770%


Trial Factoring results:
5758596061626364656667
No TF results for M4211


ECM factoring results:
Total ECM effort:61,972.550 GHz-days
Estimated T-Level:51.996
DigitsB1CompleteFacMiss
20110002,946.4330.000%
25500001,450.4190.000%
30250000505.8350.000%
351000000158.6590.000%
40300000041.6090.000%
45110000009.8000.006%
50440000002.07512.551%
551100000000.39967.084%
602600000000.07093.193%
658000000000.01298.855%
7024000000000.00299.825%


ECM Summary

B1B2factorcurvesGHz-days
30000003000000003,5239.98
1100000011000000001281.460
11000000220000000070010.58
330000009376788685603095.57
55000000193415529358660393.7
66000000153249885837250260.7
100000000271587709766333304.6
11000000024334546536301,30010,770
110000000292446636599130298.2
132000000313557390387725266.7
165000000329165764091220224.3
220000000409048655973215209.3
26000000060836419944302,36048,853
330000000804530627901010273.7
various900.6959


Lucas-Lehmer results:
No L-L results for M4211


PRP results:
dateuseridcompidcofactorsres64
2017-09-21Oliver KruseOliver-PCF7A841A91CEE8C__
2017-10-02kkmrkkblmbrbkManual testing
8423
92271433
94528529
200614777151
1898132277967
187666584810641
23076752525413563827659320172881391
F7A841A91CEE8CBF
2017-12-07ATHManual testing
8423
92271433
94528529
200614777151
1898132277967
187666584810641
23076752525413563827659320172881391
F7A841A91CEE8CBF
2020-04-17Oliver KruseIOS-1
8423
92271433
94528529
200614777151
1898132277967
187666584810641
23076752525413563827659320172881391
1CD5FB0B28CFC382
2022-05-12Jorge CoveiroManual testing
8423
1CD5FB0B28CFC382
2024-02-03Wentao HuangManual testing
8423
92271433
94528529
200614777151
1898132277967
187666584810641
23076752525413563827659320172881391
1CD5FB0B28CFC382


CERT results:
No CERT results for M4211


P-1 factor-bounds graph:
B1 = 77000000000, B2 = 774741206631261870 (P-1 stage 2)
B1 = 77000000000 (P-1 stage 1)
B1 = 100000000 (P-1 stage 1)
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109
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1016
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TF factor-bounds graph:
this exponent TF target: 44
TF double-checked to: 67
ECM T-Level=52 ~= 156-bit
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Last modified: 2024-03-13T02:15:48+00:00