is 2 4027 - 1
has 1213 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
Actual2677,378.673382.0896 %810000000008128329337432804503,191,074.723041.4520 %3,198,453.396489.5138 %
Target2440.000672.7273 %500500000.00000.9515 %0.000672.9868 %
Difference+23+7,378.6728+9.3623 %+80999999500+812832933743230450+3,191,074.7230+40.5005%+3,198,453.3958+16.5270 %

Known prime factors (3 factors, 490.9 bits, 12.19034346% known):
Remaining cofactor is not a probable-prime

P-1GHz-days
exponentfactordigitsbits*kdate foundmin B1min B2min. TFmin. P-1normal P-1
40278218576260233863807535740755696731335115.98410204341023384484489118128576728
23 × 232 × 47 × 246612745297 × 208029980948981		-2466127452972080299809489814.723e+13833.501,525.4
4027132260380788878421381488309522249241608103011475149159.856164217011160762877305051290690649666759502125
32 × 53 × 7 × 744654271 × 28003537494236854251274464137329		2020-10-01744654271280035374942368542512744641373293.659e+131.099e+202.053e+20
402755073558028420981931736977815277884416973711443146
602259410542519		65215.06568380379970723841484649835876928090907590900724045
94271096417
1483 × 2671 × 77213 × 599779 × 146988074533 × 11900314160518171 × 21310530479922829		2021-04-1911900314160518171213105304799228294.250e+13894,4431,745,161

4 Composite Factors:
P-1 results:
dateusercompB1B2BSstagefactordigitsbits*GHz-daysFac Prob
2001-02-11ANONYMOUSv4_computers1000000100000000--0.00025.156%
2001-06-09ANONYMOUSv4_computers430000004290000000--0.02037.121%
2001-06-23ANONYMOUSv4_computers30000000004290000000--0.22135.217%
2002-06-02ANONYMOUSv4_computers1073741824429000000048--0.09036.243%
2002-08-03ANONYMOUSv4_computers2147483648429000000048--0.16335.593%
2002-09-22ANONYMOUSv4_computers3221225472429000000048--0.23635.130%
2003-01-01ANONYMOUSv4_computers42900000004290000000--0.30934.760%
2023-05-16ANONYMOUSGreatLakes81000000000812832933743280450--4,068,66080.795%


Trial Factoring results:
5758596061626364656667
 BitsFactor
dateuseridcompidfromtofactorbits*digitsGHz-days
1999-09-22ANONYMOUSv4_computers2522530.149
1999-12-23ANONYMOUSv4_computers2532540.298
2000-02-09ANONYMOUSv4_computers2542550.596
2000-08-24ANONYMOUSv4_computers212562.384
2003-01-25ANONYMOUSv4_computers212574.768


ECM factoring results:
Total ECM effort:57,584.352 GHz-days
Estimated T-Level:51.935
DigitsB1CompleteFacMiss
20110003,773.2720.000%
25500001,765.8060.000%
30250000577.2430.000%
351000000170.2250.000%
40300000042.8590.000%
45110000009.7980.006%
50440000002.03513.066%
551100000000.38767.915%
602600000000.06893.435%
658000000000.01198.909%
7024000000000.00299.834%


ECM Summary

B1B2factorcurvesGHz-days
30000003000000001,5744.458
1100000011000000920.711
1100000011000000006,40973.10
1100000001100000000020022.81
11000000090051415378213.114
11000000024334546536301,1909,858
2600000003039198402256110.43
26000000060836419944302,30047,611


Lucas-Lehmer results:
No L-L results for M4027


PRP results:
dateuseridcompidcofactorsres64
2017-09-21Oliver KruseOliver-PC
82185762602338638075357407556967313
C88D2D68CF553369
2017-09-21Oliver KruseManual testing
82185762602338638075357407556967313
C88D2D68CF553369
2017-10-12kkmrkkblmbrbkManual testing
82185762602338638075357407556967313
C88D2D68CF553369
2020-04-17Oliver KruseIOS-1
82185762602338638075357407556967313
872B4531B1C5209A
2020-10-01mnd9vv
82185762602338638075357407556967313
1322603807888784213814883095222492416081030114751
872B4531B1C5209A
2020-10-02LordJuliusDarkTower
82185762602338638075357407556967313
1322603807888784213814883095222492416081030114751
872B4531B1C5209A
2021-04-19mnd950871
82185762602338638075357407556967313
1322603807888784213814883095222492416081030114751
55073558028420981931736977815277884416973711443146
602259410542519
872B4531B1C5209A
2021-04-20XZT800G3Mini2
82185762602338638075357407556967313
1322603807888784213814883095222492416081030114751
55073558028420981931736977815277884416973711443146
602259410542519
872B4531B1C5209A


CERT results:
No CERT results for M4027


P-1 factor-bounds graph:
B1 = 81000000000, B2 = 812832933743280450 (P-1 stage 2)
B1 = 81000000000 (P-1 stage 1)
B1 = 4290000000 (P-1 stage 1)
B1 = 3221225472, B2 = 4290000000 (P-1 stage 2)
B1 = 3221225472 (P-1 stage 1)
B1 = 3000000000, B2 = 4290000000 (P-1 stage 2)
B1 = 3000000000 (P-1 stage 1)
B1 = 2147483648, B2 = 4290000000 (P-1 stage 2)
B1 = 2147483648 (P-1 stage 1)
B1 = 1073741824, B2 = 4290000000 (P-1 stage 2)
B1 = 1073741824 (P-1 stage 1)
B1 = 43000000, B2 = 4290000000 (P-1 stage 2)
B1 = 43000000 (P-1 stage 1)
B1 = 1000000, B2 = 100000000 (P-1 stage 2)
B1 = 1000000 (P-1 stage 1)
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TF factor-bounds graph:
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this exponent TF target: 44
TF double-checked to: 67
ECM T-Level=51.93 ~= 156-bit
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Last modified: 2024-04-17T15:19:26+00:00