is 2 4221209 - 1
has 1270711 decimal digits
takes 0.526 GHz-days to do one PRP test
Last-known PrimeNet details:
Exponent is not assigned to anyone
factored, 0 LL tests remaining
ResidueStatus
L-L257E6847C3D32AE7double-checked
PRP-unknown--unknown-

 Trial FactoringP-1 FactoringCombined
LimitGHz-daysProbabilityB1B2GHz-daysProbabilityGHz-daysProbability
Actual2677.039265.6716 %2240001352336701.37087.0690 %8.410068.0983 %
Target2651.728364.6154 %2200022500000.02591.8765 %1.754365.2794 %
Difference+2+5.3109+1.0563 %+202000+132983670+1.3448+5.1924%+6.6557+2.8189 %

Known prime factors (1 factor, 78.1 bits, 0.00185051% known):
Remaining cofactor is not a probable-prime

P-1GHz-days
exponentfactordigitsbits*kdate foundmin B1min B2min. TFmin. P-1normal P-1
42212093270427143620232876303192478.11438738038600081551
3 × 61 × 46451 × 54517 × 83591
2013-09-16545178359121,6310.01010.0201

P-1 results:
dateusercompB1B2BSstagefactordigitsbits*GHz-daysFac Prob
2009-08-13Carsten Kossendeymother25000337500--0.0081.794%
2011-08-13Squeeky_SquirrelT7500_2200500007500006--0.0162.595%
2013-09-16Squeeky_SquirrelP4_26002478.1140.0260.000%
2023-03-07USAFSS6917th_Scty_Sq224000135233670
skipped known factor: 327042714362023287630319
--1.4478.516%


Trial Factoring results:
5758596061626364656667
 BitsFactor
dateuseridcompidfromtofactorbits*digitsGHz-days
1998-03-17ANONYMOUSv4_computers212600.018
2001-11-24David Campeauv4_computers212610.036
2011-01-27markroldgamer2612620.073
2012-01-31GrunwalderGIMPManual testing212630.378


ECM factoring results:
Total ECM effort:0.902 GHz-days
Estimated T-Level:1.154
DigitsB1CompleteFacMiss
20110000.23179.392%
25500000.02197.887%
302500000.00199.865%


ECM Summary

B1B2factorcurvesGHz-days
50000500000060.902


Lucas-Lehmer results:
dateuseridcompidres64spent (GHz-days)
2000-02-09ANONYMOUSv4_computers257E6847C3D32AE70.526


PRP results:
dateuseridcompidcofactorsres64
2017-09-20kkmrkkblmbrbkManual testing
327042714362023287630319
C3B164C5CBA55DB3
2018-01-22Oliver KruseGTX-4
327042714362023287630319
C3B164C5CBA55DB3


CERT results:
No CERT results for M4221209


P-1 factor-bounds graph:
B1 = 224000, B2 = 135233670 (P-1 stage 2)
B1 = 224000 (P-1 stage 1)
B1 = 50000, B2 = 750000 (P-1 stage 2)
B1 = 50000 (P-1 stage 1)
B1 = 25000, B2 = 337500 (P-1 stage 2)
B1 = 25000 (P-1 stage 1)
103
104
105
106
103
104
105
106
107
108
109
TF factor-bounds graph:
263
262
261
260
this exponent TF target: 65
TF double-checked to: 67
ECM T-Level=1.15 ~= -13-bit
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Last modified: 2024-03-13T02:15:48+00:00