M1953811 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	2⁶⁸	30.5070	69.1176%	1953811	244226375	1.1920	8.4450%	31.6990	71.7257%	2.6080%
PrimeNet	2⁵⁸	0.0197	63.7931%	8000	140000	0.0012	2.4677%	0.0208	64.6866%	0.8935%
GPU72	2⁶²	0.3144	66.1290%	8000	90000	0.0010	1.1536%	0.3154	66.5198%	0.3907%
Difference	+6	+30.1925	+2.9886%	+1945811	+244136375	+1.1910	+7.2915%	+31.3836	+5.2059%	+5.2059%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1953811	121357642481425389993327431	27	86.649	31056648386518806065 5 × 7 × 19 × 46701726897020761	2020-02-24	19	46701726897020761	8,446,331	200,151,926	373,828,059

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	25000	387500		-		-	-	0.004	-	-	1.051%
2011-05-16T22:44:00	kurly	hex	1000000	30000000		-		-	-	0.203	-	-	5.697%
2018-01-22T03:17:36	Jocelyn Larouche	low 4M	1953811	60000000	12	-		-	-	0.402	-	-	6.835%
2018-03-03T03:57:56	Jocelyn Larouche	low 4M	1953811	120000000	12	-		-	-	0.660	-	-	7.627%
2018-05-11T11:44:16	Jocelyn Larouche	low 4M	1953811	195381100	12	-		-	-	0.983	-	-	8.188%
2018-11-26T12:54:02	Jocelyn Larouche	Manual testing	1953811	244226375	12	-		-	-	1.192	-	-	8.445%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1998-12-21T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.020	-	-
2016-02-23T16:29:00	Mark Rose	Manual testing	2⁵⁸	2⁶⁰		-	-	0.059	-	-
2010-01-16T20:20:00	S485122	USB-W	2⁶⁰	2⁶¹		-	-	0.079	-	-
2016-02-23T16:29:00	Mark Rose	Manual testing	2⁶¹	2⁶²		-	-	0.157	-	-
2011-08-27T22:19:00	GrunwalderGIMP	Manual testing	2¹	2⁶³		-	-	0.817	-	-
2016-02-23T16:29:00	Mark Rose	Manual testing	2⁶²	2⁶³		-	-	0.502	-	-
2015-04-22T20:23:00	lycorn	Manual testing	2⁶³	2⁶⁴		-	-	1.005	-	-
2015-04-22T20:23:00	lycorn	Manual testing	2⁶⁴	2⁶⁵		-	-	1.912	-	-
2015-09-07T08:31:00	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	3.825	-	-
2018-02-05T16:30:32	TJAOI	Manual testing	2⁶⁶	2⁶⁷		-	-	7.649	-	-
2019-05-13T04:32:11	chuenkit	Manual testing	2⁶⁷	2⁶⁸		-	-	15.30	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	19.779 GHz-days
Estimated T-Level:	24.482

Digits	B1	Curves	Complete	FacMiss
20	11000	251 / 100	2.510	8.025%
25	50000	251 / 280	0.896	40.737%

New Calculation Method

Total ECM effort:	19.779 GHz-days
Estimated T-Level:	24.482

Digits	B1	Complete	FacMiss
20	11000	8.667	0.017%
25	50000	0.773	46.168%
30	250000	0.048	95.328%
35	1000000	0.002	99.780%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		83	5.776
50000	5000000	121357642481425389993327431	3	0.209
50000	7500000		165	13.79

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2008-11-20T05:53:00	ClknGo Software	plms3	50000	5000000						3	0.209
2009-08-15T12:12:00	SubPrime	abd0	50000	5000000						3	0.209
2011-01-19T20:09:00	Csaba Vágó	timigep	50000	5000000						3	0.209
2012-11-26T04:50:00	Donna Noble	CCI_PH2_955	50000	5000000						3	0.209
2014-01-01T21:02:00	Andy Incline	Office-PC	50000	5000000						3	0.209
2015-05-13T16:08:00	Sergiosi	Manual testing	50000	5000000						5	0.348
2016-02-26T19:13:34	Bruce	Desk6	50000	5000000						3	0.209
2016-05-30T07:23:43	Bruce	Desk6	50000	5000000						3	0.209
2016-08-11T23:25:24	Bruce	test	50000	5000000						3	0.209
2017-01-31T13:54:24	Bruce	Desk6	50000	5000000						3	0.209
2017-07-13T20:24:42	Bruce	Desk6	50000	5000000						3	0.209
2017-12-04T17:27:11	Bruce	Desk6	50000	5000000						3	0.209
2018-04-07T15:34:50	Bruce	Desk6	50000	5000000						3	0.209
2018-09-18T09:27:07	Bruce	Desk6	50000	5000000						3	0.209
2019-12-07T17:49:00	Corey	Computer	50000	5000000						3	0.209
2019-12-09T19:22:16	Yuji HASEGAWA	sx1w7	50000	5000000						3	0.209
2019-12-14T02:27:02	mnd9	75211cornerb	50000	5000000						3	0.209
2019-12-19T03:15:47	daveward2005	Davy	50000	5000000						3	0.209
2019-12-25T23:23:46	mnd9	50871b	50000	5000000						3	0.209
2019-12-30T23:54:16	cappy95833	HomePC	50000	5000000						3	0.209
2020-01-04T20:06:10	Alvin Bunk	BADCAT	50000	5000000						3	0.209
2020-01-11T18:26:57	Keysarecool	Boat_Anchor	50000	5000000						3	0.209
2020-01-19T11:16:51	daveward2005	Davy	50000	5000000						3	0.209
2020-01-24T18:45:23	daveward2005	MW	50000	5000000						3	0.209
2020-02-02T11:39:47	David_McCann	i5	50000	5000000						3	0.209
2020-02-11T00:29:26	EricP	Cannonfodder	50000	5000000						3	0.209
2020-02-18T12:25:00	daveward2005	MW	50000	5000000						3	0.209
2020-02-25T02:53:33	Keysarecool	Boat_Anchor	50000	5000000	121357642481425389993327431	86.649	3	2	303014763332831	3	0.209
2022-05-05T09:33:01	TJAOI	Manual testing	50000	7500000						165	13.79

date	userid	compid	res64	spent (GHz-days)
1999-01-10T00:00:00	ANONYMOUS	v4_computers	B96A81413F6628C1	0.106
2015-07-12T18:10:00	MadPoo	Manual testing	B96A81413F6628C1	0.106

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 = 1953811, B2 = 244226375 (P-1 stage 2)

B1 = 1953811, B2 = 195381100 (P-1 stage 2)

B1 = 1953811, B2 = 120000000 (P-1 stage 2)

B1 = 1953811, B2 = 60000000 (P-1 stage 2)

B1 = 1000000, B2 = 30000000 (P-1 stage 2)

B1 = 1953811 (P-1 stage 1)

B1 = 1000000 (P-1 stage 1)

B1 = 25000, B2 = 387500 (P-1 stage 2)

B1 = 25000 (P-1 stage 1)

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

10¹²

10¹³

10¹⁴

10¹⁵

10¹⁶

10¹⁷

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