M559877 Mersenne number exponent details

	Trial Factoring	P-1 Factoring	Combined
Limit	GHz-days	Probability	B1	B2	GHz-days	Probability	GHz-days	Probability	Prob over default TF
Actual	2⁶⁷	53.0722	70.1493%	15000000	1815000000	2.3909	12.1713%	55.4632	73.7825%	3.6332%
PrimeNet	2⁴⁰	0.0000	50.0000%	5500	190000	0.0003	19.8120%	0.0003	59.9060%	9.9060%
GPU72	2⁴⁴	0.0000	54.5455%	10000	320000	0.0006	15.0176%	0.0006	61.3716%	6.8262%
Difference	+23	+53.0722	+15.6038%	+14990000	+1814680000	+2.3904	-2.8463%	+55.4626	+12.4109%	+12.4109%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
559877	135524652208475035572923023	27	86.809	121030737294508468443 3² × 17 × 149 × 5309064231894919	2013-09-18	149	5309064231894919	42,549,830	6,116,484	11,423,890

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2001-12-22T00:00:00	ANONYMOUS	v4_computers	2000	200000		-		-	-	0.000	-	-	0.183%
2002-01-22T00:00:00	ANONYMOUS	v4_computers	4096	409600		-		-	-	0.001	-	-	0.397%
2002-03-03T00:00:00	ANONYMOUS	v4_computers	8192	819200		-		-	-	0.001	-	-	0.724%
2002-04-28T00:00:00	ANONYMOUS	v4_computers	16384	1638400		-		-	-	0.002	-	-	1.187%
2002-06-29T00:00:00	ANONYMOUS	v4_computers	32768	3276800		-		-	-	0.004	-	-	1.793%
2002-09-14T00:00:00	ANONYMOUS	v4_computers	65536	6553600		-		-	-	0.009	-	-	2.540%
2003-05-19T00:00:00	ANONYMOUS	v4_computers	131072	13107200		-		-	-	0.018	-	-	3.415%
2011-06-25T17:15:00	Jocelyn Larouche	Manual testing	362144	362144		-		-	-	0.008	-	-	1.437%
2011-08-20T14:17:00	Jocelyn Larouche	Manual testing	704779	704779		-		-	-	0.015	-	-	1.935%
2012-03-05T12:57:00	Jocelyn Larouche	Manual testing	880974	880974		-		-	-	0.019	-	-	2.122%
2012-07-14T15:57:00	Jocelyn Larouche	Manual testing	1119754	1119754		-		-	-	0.024	-	-	2.333%
2012-10-12T21:13:00	Jocelyn Larouche	Manual testing	3586991	3586991		-		-	-	0.076	-	-	3.516%
2016-03-17T18:48:47	alpertron	Manual testing	1500000	50000000	12	-		-	-	0.088	-	-	6.175%
2021-08-13T09:26:50	ViliamF	3	15000000	1815000000		-		-	-	2.391	-	-	12.171%

	Bits	Factor	GHz-Days	worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved
2000-04-05T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁴		-	-	0.004	-	-
2022-03-07T08:27:20	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		-	-	0.034	-	-
2003-12-13T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.069	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	17.296 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:	17.296 GHz-days
Estimated T-Level:	26.125

Digits	B1	Complete	FacMiss
20	11000	24.769	0.000%
25	50000	3.131	4.366%
30	250000	0.300	74.067%
35	1000000	0.023	97.712%
40	3000000	0.001	99.851%

ECM Summary

B1	B2	factor	curves	GHz-days
		135524652208475035572923023	1	0.00000e+0
50000	5000000		280	4.529
250000	25000000		44	3.559
250000	35000000		100	9.208

ECM Details

										GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2007-08-20T00:33:00	Chad Davis	Bayes	50000	5000000						1	0.016
2007-09-27T02:50:00	James Heinrich	WHS	50000	5000000						1	0.016
2008-01-14T23:31:00	Steve Scott	Gigabyte-1	50000	5000000						3	0.049
2008-08-20T21:33:00	Sturle Sunde	v22	50000	5000000						3	0.049
2008-10-25T17:16:00	Jayson King	atlas	50000	5000000						3	0.049
2009-01-02T17:01:00	Sturle Sunde	v17	50000	5000000						3	0.049
2009-03-03T17:40:00	Sturle Sunde	v23	50000	5000000						3	0.049
2009-04-17T08:38:00	Sturle Sunde	v26	50000	5000000						3	0.049
2009-07-03T17:23:00	Architects Cubed	m1_53	50000	5000000						3	0.049
2009-07-10T10:01:00	Architects Cubed	m1_02	50000	5000000						3	0.049
2009-08-19T14:13:00	linded	KCPB8P0-NET214	50000	5000000						3	0.049
2009-09-21T21:05:00	Sturle Sunde	TOR-ST-0017	50000	5000000						3	0.049
2009-10-17T20:12:00	Sturle Sunde	TOR-ST-0020	50000	5000000						3	0.049
2009-11-03T09:39:00	linded	KCPB8P0-NET214	50000	5000000						3	0.049
2009-11-20T03:22:00	Sturle Sunde	FKWXPTESTEIK	50000	5000000						3	0.049
2009-12-11T19:36:00	Sturle Sunde	FLB-ST-0037	50000	5000000						3	0.049
2010-01-01T16:50:00	Sturle Sunde	FKWXPTESTEIK	50000	5000000						3	0.049
2010-01-20T02:28:00	James Hintz	03_122109	50000	5000000						3	0.049
2010-02-16T16:31:00	Sturle Sunde	FKWXPTESTEIK	50000	5000000						3	0.049
2010-03-08T14:53:00	Lackó	Iroda_Andras	50000	5000000						3	0.049
2010-03-09T18:24:00	Sturle Sunde	FKWXPTESTEIK	50000	5000000						3	0.049
2010-03-26T01:52:00	Sturle Sunde	TOR-ST-0027	50000	5000000						3	0.049
2010-04-11T20:35:00	Sturle Sunde	FKWXPTESTEIK	50000	5000000						3	0.049
2010-04-27T19:13:00	Sturle Sunde	FKWXPTESTEIK	50000	5000000						3	0.049
2010-05-15T22:33:00	Sturle Sunde	FKWXPTESTEIK	50000	5000000						3	0.049
2010-06-02T17:03:00	Sturle Sunde	PRE6S32KN9Z73F9	50000	5000000						3	0.049
2010-06-24T01:07:00	Sturle Sunde	FKWXPTESTEIK	50000	5000000						3	0.049
2010-07-20T16:25:00	Sturle Sunde	FKWXPTESTEIK	50000	5000000						3	0.049
2010-08-15T00:34:00	Sturle Sunde	FKWXPTESTEIK	50000	5000000						3	0.049
2010-09-03T23:28:00	Sturle Sunde	TOR-ST-0017	50000	5000000						3	0.049
2010-09-19T05:20:00	sannerud.com	Jim2010	50000	5000000						3	0.049
2010-10-05T18:58:00	Sturle Sunde	FKWXPTESTEIK	50000	5000000						3	0.049
2010-10-20T02:58:00	Sturle Sunde	PRECZB31311N6	50000	5000000						3	0.049
2010-11-02T13:48:00	sannerud.com	Jim2010	50000	5000000						3	0.049
2010-11-18T22:06:00	Sturle Sunde	FKWXPTESTEIK	50000	5000000						3	0.049
2010-12-04T04:45:00	Sturle Sunde	FKWXPTESTEIK	50000	5000000						3	0.049
2010-12-15T21:39:00	Sturle Sunde	FKWXPTESTEIK	50000	5000000						3	0.049
2011-01-05T11:52:00	James Hintz	06_122109	50000	5000000						3	0.049
2011-01-16T20:11:00	Sturle Sunde	FKWXPTESTEIK	50000	5000000						3	0.049
2011-01-29T00:26:00	Sturle Sunde	FKWXPTESTEIK	50000	5000000						3	0.049
2011-02-14T03:57:00	Sturle Sunde	FKWXPTESTEIK	50000	5000000						3	0.049
2011-02-25T20:39:00	Sturle Sunde	PREUSW40604NL	50000	5000000						3	0.049
2011-03-09T03:56:00	Sturle Sunde	FKWXPTESTEIK	50000	5000000						3	0.049
2011-04-09T10:20:00	Damian Silvestre	PcMa	50000	5000000						3	0.049
2011-04-29T01:45:00	Sturle Sunde	FKWXPTESTEIK	50000	5000000						3	0.049
2011-05-17T16:59:00	Sturle Sunde	FKWXPTESTEIK	50000	5000000						3	0.049
2011-05-21T07:40:00	Lukasz Wrobel	w-l	50000	5000000						3	0.049
2011-05-31T15:33:00	Sturle Sunde	FKWXPTESTEIK	50000	5000000						3	0.049
2011-06-17T20:16:00	Sturle Sunde	FKWXPTESTEIK	50000	5000000						3	0.049
2011-07-13T02:27:00	Netanias	NCS2009Fermat	50000	5000000						3	0.049
2011-08-06T22:19:00	Lukasz Wrobel	w-l	50000	5000000						3	0.049
2011-09-09T03:31:00	Sturle Sunde	FKWXPTESTEIK	50000	5000000						3	0.049
2011-11-13T05:56:00	Sturle Sunde	PRE0011254B6EE4	50000	5000000						3	0.049
2012-01-06T03:24:00	Sturle Sunde	FKWXPTESTEIK	50000	5000000						3	0.049
2012-02-16T03:01:00	Sturle Sunde	FKWXPTESTEIK	50000	5000000						3	0.049
2012-04-02T00:15:00	Sturle Sunde	TOR-ST-0036	50000	5000000						3	0.049
2012-06-10T12:32:00	Jacques MOLNE	Orlinde_knight	50000	5000000						3	0.049
2012-08-26T00:17:00	Sturle Sunde	PRECZC5060K5N	50000	5000000						3	0.049
2013-02-28T18:25:00	Lukasz Wrobel	v7	50000	5000000						3	0.049
2013-09-18T08:29:00	lopper	Surface_staples			135524652208475035572923023	86.809		1		1	-
2016-04-01T10:53:43	TJAOI	Manual testing	50000	5000000						16	0.259
2016-10-14T16:22:29	TJAOI	Manual testing	50000	5000000						91	1.472
2018-11-23T13:31:57	TJAOI	Manual testing	250000	25000000						44	3.559
2021-09-29T12:05:58	TJAOI	Manual testing	250000	35000000						100	9.208

date	userid	compid	res64	spent (GHz-days)
2002-06-15T00:00:00	ANONYMOUS	v4_computers	2D42B8F01FABDDC7	0.008

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 = 15000000, B2 = 1815000000 (P-1 stage 2)

B1 = 15000000 (P-1 stage 1)

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

B1 = 3586991 (P-1 stage 1)

B1 = 1500000 (P-1 stage 1)

B1 = 1119754 (P-1 stage 1)

B1 = 880974 (P-1 stage 1)

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

B1 = 704779 (P-1 stage 1)

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

B1 = 362144 (P-1 stage 1)

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

B1 = 131072 (P-1 stage 1)

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

B1 = 65536 (P-1 stage 1)

B1 = 8192, B2 = 819200 (P-1 stage 2)

B1 = 32768 (P-1 stage 1)

B1 = 4096, B2 = 409600 (P-1 stage 2)

B1 = 16384 (P-1 stage 1)

B1 = 2000, B2 = 200000 (P-1 stage 2)

B1 = 8192 (P-1 stage 1)

B1 = 4096 (P-1 stage 1)

B1 = 2000 (P-1 stage 1)

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

10¹²

10¹³

10¹⁴

10¹⁵

10¹⁶

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