M2618881 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	2⁶⁹	45.5869	68.1159%	2618881	26188810	0.4371	5.6951%	46.0241	69.9318%	1.8158%
PrimeNet	2⁵⁹	0.0293	62.7119%	11000	200000	0.0024	2.6985%	0.0317	63.7181%	1.0062%
GPU72	2⁶³	0.6094	65.0794%	12000	200000	0.0025	1.5325%	0.6119	65.6145%	0.5352%
Difference	+6	+44.9775	+3.0366%	+2606881	+25988810	+0.4346	+4.1625%	+45.4121	+4.3172%	+4.3172%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2618881	869446454998177536120647977	27	89.490	165995792668352921748 2² × 3 × 1181 × 146347 × 80035398697	2021-09-23	146347	80035398697	86,294,423	488.36	912.10

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2003-10-31T00:00:00	ANONYMOUS	v4_computers	2048	204800		-		-	-	0.001	-	-	0.192%
2003-11-08T00:00:00	Team Prime Rib	v4_computers	15000	217500		-		-	-	0.003	-	-	0.667%
2010-11-17T22:12:00	Jocelyn Larouche	Manual testing	20000	20000		-		-	-	0.002	-	-	0.223%
2010-12-12T11:23:00	markr	tiny	100000	2125000		-		-	-	0.024	-	-	2.194%
2014-10-13T22:29:00	Jocelyn Larouche	Manual testing	124508	124508		-		-	-	0.014	-	-	0.819%
2016-05-24T01:15:57	Jocelyn Larouche	Manual testing	200000	3600000	6	-		-	-	0.043	-	-	2.826%
2017-07-20T22:03:19	Jocelyn Larouche	low 4M	400000	4000000	6	-		-	-	0.067	-	-	3.195%
2019-10-14T15:57:33	masser	Manual testing	2618881	26188810	12	-		-	-	0.437	-	-	5.695%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1999-03-26T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁹		-	-	0.029	-	-
2016-02-23T16:29:17	Mark Rose	Manual testing	2⁵⁹	2⁶⁰		-	-	0.029	-	-
2009-01-30T23:44:00	Sturle Sunde	giovanni.ifi	2⁶⁰	2⁶¹		-	-	0.059	-	-
2012-06-18T09:08:00	markr	oldgamer	2⁶¹	2⁶²		-	-	0.117	-	-
2013-01-14T11:57:00	dbaugh	Manual testing	2⁶²	2⁶³		-	-	0.375	-	-
2015-02-18T11:41:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.750	-	-
2015-02-18T11:41:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.427	-	-
2016-01-17T23:07:15	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	2.853	-	-
2017-08-30T11:24:05	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	5.707	-	-
2019-04-15T13:43:00	TJAOI	Manual testing	2⁶⁷	2⁶⁸		-	-	11.41	-	-
2021-05-19T10:50:02	TJAOI	Manual testing	2⁶⁸	2⁶⁹		-	-	22.83	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	12.959 GHz-days
Estimated T-Level:	22.161

Digits	B1	Curves	Complete	FacMiss
20	11000	121 / 100	1.210	29.639%
25	50000	121 / 280	0.432	64.861%

New Calculation Method

Total ECM effort:	12.959 GHz-days
Estimated T-Level:	22.161

Digits	B1	Complete	FacMiss
20	11000	3.996	1.840%
25	50000	0.365	69.450%
30	250000	0.023	97.750%
35	1000000	0.001	99.894%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		107	11.03
50000	5000000	869446454998177536120647977	2	0.206
50000	6750000		7	0.829
76620	10000000		5	0.893

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-02-27T13:39:00	Never Odd Or Even	T_Quad	50000	5000000						3	0.309
2010-06-12T19:30:00	Lupo	yorick	50000	5000000						3	0.309
2012-11-22T11:08:00	GrunwalderGIMP	vangelis	50000	5000000						3	0.309
2014-09-13T16:38:00	arnaud	srv-630	50000	5000000						3	0.309
2015-11-26T11:59:52	lopper	i5-4670	50000	5000000						3	0.309
2016-03-28T21:52:36	Jason U	Server7	50000	5000000						3	0.309
2016-09-22T03:50:35	lettp	Home	50000	5000000						3	0.309
2017-06-19T17:35:28	Marius Zens	KBWR_TV3	50000	5000000						3	0.309
2017-10-26T18:22:21	Sebastian Hornbostel	V2	50000	5000000						3	0.309
2018-04-23T00:19:57	Chang Chia-Tche	ex-ctcpc	50000	5000000						3	0.309
2019-03-03T07:35:49	Chang Chia-Tche	ex-ctcpc	50000	5000000						3	0.309
2020-07-07T18:28:06	GAN	LMS-06	50000	5000000						3	0.309
2020-07-14T15:33:55	Oliver Kruse	Krusen-NAS	50000	5000000						3	0.309
2020-07-20T01:14:43	GAN	LMS-07	50000	5000000						3	0.309
2020-07-26T10:03:26	GAN	LMS-11	50000	5000000						3	0.309
2020-08-02T17:47:02	GAN	LMS-18	50000	5000000						3	0.309
2020-08-10T12:26:38	GAN	LMS-18	50000	5000000						3	0.309
2020-08-25T05:06:33	M. R. Mayer	nimbus	50000	5000000						7	0.722
2020-09-28T15:43:24	mnd9	25836b	50000	5000000						7	0.722
2020-10-25T05:28:16	Chang Chia-Tche	ex-ctcpc	50000	5000000						7	0.722
2020-11-28T20:27:53	RIHATEC	i7-3770K	50000	5000000						7	0.722
2020-12-13T10:41:45	Bruno Victal	Manual testing	76620	10000000						5	0.893
2021-02-10T21:34:52	Zenzoma	AM3700X_1	50000	5000000						7	0.722
2021-03-12T01:08:33	Gerry Snyder	Gerry-Workstation	50000	5000000						7	0.722
2021-04-18T08:27:43	Zenzoma	AM3700X_1	50000	5000000						7	0.722
2021-06-12T05:56:31	GAN	KL-SCH07	50000	5000000						7	0.722
2021-07-21T00:00:44	kutens	vega	50000	6750000						7	0.829
2021-09-23T09:46:31	GAN	KL-SCH02	50000	5000000	869446454998177536120647977	89.490	2	2	292322608333763	2	0.206

date	userid	compid	res64	spent (GHz-days)
1999-07-26T00:00:00	ANONYMOUS	v4_computers	D8C2E9AA3128BDA4	0.202
2000-04-27T00:00:00	ANONYMOUS	v4_computers	D8C2E9AA3128BDA4	0.202
2018-07-07T08:55:19	kkmrkkblmbrbk	old	D8C2E9AA3128BDA4	0.202

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 = 2618881, B2 = 26188810 (P-1 stage 2)

B1 = 2618881 (P-1 stage 1)

B1 = 400000, B2 = 4000000 (P-1 stage 2)

B1 = 400000 (P-1 stage 1)

B1 = 200000, B2 = 3600000 (P-1 stage 2)

B1 = 100000, B2 = 2125000 (P-1 stage 2)

B1 = 200000 (P-1 stage 1)

B1 = 124508 (P-1 stage 1)

B1 = 100000 (P-1 stage 1)

B1 = 15000, B2 = 217500 (P-1 stage 2)

B1 = 20000 (P-1 stage 1)

B1 = 15000 (P-1 stage 1)

B1 = 2048, B2 = 204800 (P-1 stage 2)

B1 = 2048 (P-1 stage 1)

10²

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10¹¹

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