M555857 Mersenne number exponent details

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M555857

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is 2 ⁵⁵⁵⁸⁵⁷ - 1

has 167330 decimal digits

takes 0.008 GHz-days to do one PRP test

Last-known PrimeNet details:

Exponent is not assigned to anyone

0 primality tests remaining

	Residue	Status
L-L	2D1540D56E9A19__	double-checked
PRP	-unknown-	-unknown-

	Trial Factoring			P-1 Factoring				Combined
	Limit	GHz-days	Probability	B1	B2	GHz-days	Probability	GHz-days	Probability	Prob over default TF
Actual	2⁶⁷	53.4560	70.1493%	1500000	50000000	0.0876	6.1700%	53.5436	71.9911%	1.8418%
PrimeNet	2⁴⁰	0.0000	50.0000%	5500	190000	0.0003	19.7956%	0.0003	59.8978%	9.8978%
GPU72	2⁴⁴	0.0000	54.5455%	10000	320000	0.0006	15.0044%	0.0006	61.3657%	6.8202%
Difference	+23	+53.4560	+15.6038%	+1490000	+49680000	+0.0870	-8.8344%	+53.5431	+10.6254%	+10.6254%

Known prime factors (2 factors, 147.2 bits, 0.02648467% known):

Remaining cofactor is not a probable-prime

						P-1		GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
555857	1847679796326042922007	22	70.646	1662010010061979 101 × 4159 × 3956610881	2016-03-24	4159	3956610881	576.91	4.5584	8.5137
555857	112220813480075676829433	24	76.571	100943959939404988 2² × 7 × 303539 × 11877028739	2008-01-14	303539	11877028739	32,705	13.689	25.557

1 Composite Factors:

exponent	prime factors	composite factor	digits	bits*
555857	1847679796326042922007 112220813480075676829433	207348129794409078565815100384624560661032031	45	147.217

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2000-12-07T00:00:00	Alex Kruppa	v4_computers	100000	4000000		-		-	-	0.007	-	-	2.538%
2002-05-05T00:00:00	ANONYMOUS	v4_computers	16384	1638400		-		-	-	0.002	-	-	1.185%
2002-06-29T00:00:00	ANONYMOUS	v4_computers	32768	3276800		-		-	-	0.004	-	-	1.791%
2002-09-07T00:00:00	ANONYMOUS	v4_computers	65536	6553600		-		-	-	0.009	-	-	2.537%
2003-05-11T00:00:00	ANONYMOUS	v4_computers	131072	13107200		-		-	-	0.018	-	-	3.411%
2016-03-17T18:48:42	alpertron	Manual testing	1500000	50000000	12	-		-	-	0.088	-	-	6.170%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2000-03-27T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁴		-	-	0.004	-	-
2022-03-07T08:27:13	LordJulius	Manual testing	2⁵⁴	2⁵⁵		-	-	0.004	-	-
2001-04-08T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁶		-	-	0.017	-	-
2002-01-15T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁷		-	-	0.035	-	-
2003-12-13T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.069	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	16.168 GHz-days
Estimated T-Level:	26.125

Digits	B1	Curves	Complete	FacMiss
20	11000	424 / 100	4.240	1.410%
25	50000	424 / 280	1.514	21.937%
30	250000	144 / 640	0.225	79.838%

New Calculation Method

Total ECM effort:	16.168 GHz-days
Estimated T-Level:	26.125

Digits	B1	Complete	FacMiss
20	11000	23.860	0.000%
25	50000	3.025	4.858%
30	250000	0.287	75.066%
35	1000000	0.022	97.833%
40	3000000	0.001	99.860%

ECM Summary

B1	B2	factor	curves	GHz-days
		112220813480075676829433	1	0.00000e+0
50000	5000000		278	4.495
50000	5000000	1847679796326042922007	2	0.032
250000	25000000		144	11.64

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2007-08-20T09:27:00	drew	messier	50000	5000000						1	0.016
2007-09-25T15:45:00	Chad Davis	Bayes	50000	5000000						1	0.016
2008-01-14T12:05:00	Team_Bundu	bundu1			112220813480075676829433	76.571		1		1	-
2015-05-22T12:21:00	Richard B. Woods	Puttputt	50000	5000000						2	0.032
2015-07-31T09:47:00	TJAOI	Manual testing	50000	5000000						95	1.536
2016-03-24T20:23:54	TJAOI	Manual testing	50000	5000000						88	1.423
2016-03-24T20:23:54	TJAOI	Manual testing	50000	5000000	1847679796326042922007	70.646	2	2		2	0.032
2016-07-22T12:42:49	TJAOI	Manual testing	50000	5000000						91	1.471
2018-07-27T12:37:52	TJAOI	Manual testing	250000	25000000						44	3.557
2021-02-12T10:25:18	TJAOI	Manual testing	250000	25000000						100	8.084

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
2002-05-25T00:00:00	ANONYMOUS	v4_computers	2D1540D56E9A19__	0.008

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-27T10:55:40

Oliver Kruse

GTX-3

1847679796326042922007

112220813480075676829433

3D4B3A8EF66E239A

2017-09-28T09:43:12

Oliver Kruse

Manual testing

1847679796326042922007

112220813480075676829433

3D4B3A8EF66E23__

2017-10-13T15:31:25

kkmrkkblmbrbk

c4.xlarge

3D4B3A8EF66E23__

2020-04-19T06:31:44

Oliver Kruse

AddPrpType5

1847679796326042922007

112220813480075676829433

6400696316D624__

P-1 factor-bounds graph:

X = B1; Y = B2
size of marker relates to size of factor
mouse-over any factor marker (circle) to see additional info
mouse-over any stage bound text to see additional info

B1 = 1500000, B2 = 50000000 (P-1 stage 2)

B1 = 1500000 (P-1 stage 1)

B1 = 131072, B2 = 13107200 (P-1 stage 2)

B1 = 65536, B2 = 6553600 (P-1 stage 2)

B1 = 100000, B2 = 4000000 (P-1 stage 2)

B1 = 32768, B2 = 3276800 (P-1 stage 2)

B1 = 131072 (P-1 stage 1)

B1 = 16384, B2 = 1638400 (P-1 stage 2)

B1 = 100000 (P-1 stage 1)

B1 = 65536 (P-1 stage 1)

B1 = 32768 (P-1 stage 1)

B1 = 16384 (P-1 stage 1)

10²

10³

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10⁵

10⁶

10⁷

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

TF factor-bounds graph:

2⁶⁷

2⁵⁸

2⁵⁷

2⁵⁶

2⁵⁵

2⁵⁴

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

Last modified: 2022-03-07T08:27:13+00:00

0M	<	10¹⁰	All tracked exponents
0M	<	2³²	GPU TF range
0M	<	1000M	PrimeNet range
0M	<	193M	low-PrimeNet, low-res
0M	<	385M	low-PrimeNet, high-res
50M	<	146M	PrimeNet wavefront