M2054471 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	29.0123	69.1176%	3600000	180000000	1.2595	8.5629%	30.2718	71.7621%	2.6444%
PrimeNet	2⁵⁸	0.0187	63.7931%	9000	160000	0.0016	2.6667%	0.0203	64.7586%	0.9655%
GPU72	2⁶²	0.2990	66.1290%	9000	120000	0.0014	1.3309%	0.3005	66.5798%	0.4508%
Difference	+6	+28.7132	+2.9886%	+3591000	+179880000	+1.2580	+7.2320%	+29.9713	+5.1822%	+5.1822%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2054471	41425672179242665817311	23	75.133	10081834248145305 3 × 5 × 487 × 1380127891601	2020-06-29	487	1380127891601	4,679.9	7,168.7	13,389

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2003-02-24T00:00:00	ANONYMOUS	v4_computers	2048	204800		-		-	-	0.001	-	-	0.222%
2006-01-15T00:00:00	Jocelyn Larouche	v4_computers	4000	4000		-		-	-	0.000	-	-	0.047%
2009-05-24T19:26:00	Rob_Dee	twopc	20000	280000		-		-	-	0.003	-	-	0.893%
2010-12-26T02:29:00	Jocelyn Larouche	Manual testing	30000	30000		-		-	-	0.003	-	-	0.350%
2011-01-06T01:06:00	Jocelyn Larouche	Manual testing	50000	50000		-		-	-	0.005	-	-	0.508%
2011-01-21T07:54:00	James Heinrich	i7-920	135000	2902500		-		-	-	0.027	-	-	2.716%
2014-10-26T00:59:00	Jocelyn Larouche	Manual testing	166241	166241		-		-	-	0.016	-	-	1.058%
2016-05-15T21:00:26	Jocelyn Larouche	Manual testing	270000	4860000	6	-		-	-	0.050	-	-	3.413%
2016-09-22T12:02:51	Jocelyn Larouche	low 4M	270000	5832000	6	-		-	-	0.055	-	-	3.550%
2016-11-06T00:28:17	Jocelyn Larouche	low 4M	324000	324000		-		-	-	0.031	-	-	1.482%
2017-01-29T16:31:00	mikr	MSI	2500000	125000000	12	-		-	-	0.875	-	-	7.881%
2017-02-24T12:35:57	mikr	S052	3600000	180000000	12	-		-	-	1.259	-	-	8.563%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2016-02-23T16:29:04	Mark Rose	Manual testing	2¹	2⁶⁰		-	-	0.075	-	-
2009-01-02T10:16:00	Sturle Sunde	gorky.ifi	2⁶⁰	2⁶¹		-	-	0.075	-	-
2012-03-11T11:47:00	Sebastian Hornbostel	Manual testing	2⁶¹	2⁶²		-	-	0.150	-	-
2013-09-01T20:20:00	ramgeis	Manual testing	2⁶²	2⁶³		-	-	0.478	-	-
2015-04-21T09:19:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.956	-	-
2015-04-21T09:19:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.819	-	-
2015-11-03T10:10:00	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	3.637	-	-
2016-08-18T20:55:11	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	7.275	-	-
2019-03-24T00:15:07	chuenkit	Manual testing	2⁶⁷	2⁶⁸		-	-	14.55	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	8.911 GHz-days
Estimated T-Level:	21.875

Digits	B1	Curves	Complete	FacMiss
20	11000	105 / 100	1.050	34.809%
25	50000	105 / 280	0.375	68.683%

New Calculation Method

Total ECM effort:	8.911 GHz-days
Estimated T-Level:	21.875

Digits	B1	Complete	FacMiss
20	11000	3.387	3.381%
25	50000	0.306	73.630%
30	250000	0.019	98.133%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		102	8.656
50000	5000000	41425672179242665817311	3	0.255

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2008-12-07T04:27:00	Matthias Eckoldt	serverSP	50000	5000000						3	0.255
2009-10-25T23:37:00	SubPrime	stor	50000	5000000						3	0.255
2011-04-14T09:23:00	James Hintz	ryan	50000	5000000						3	0.255
2013-03-06T23:10:00	Donna Noble	PH2x6	50000	5000000						3	0.255
2014-04-01T07:53:00	OS1	L3	50000	5000000						3	0.255
2015-07-12T17:28:00	guru	w1	50000	5000000						3	0.255
2016-02-18T23:48:19	Sintax	cloud2	50000	5000000						3	0.255
2016-05-05T15:57:08	Bruce	Desk6	50000	5000000						3	0.255
2016-07-17T19:52:54	Bruce	test	50000	5000000						3	0.255
2016-12-16T01:01:48	Bruce	Desk6	50000	5000000						3	0.255
2017-06-30T12:11:02	Bruce	Desk6	50000	5000000						3	0.255
2017-12-02T12:57:49	Conductor	Andrew	50000	5000000						3	0.255
2018-04-12T21:31:57	Bruce	Desk6	50000	5000000						3	0.255
2018-10-01T00:25:57	storm5510	7700_Kaby_Lake	50000	5000000						3	0.255
2019-12-27T16:01:19	MarkS	desktop-i7	50000	5000000						3	0.255
2020-01-01T02:36:58	Keysarecool	HPLaptop	50000	5000000						3	0.255
2020-01-07T23:43:06	mnd9	kitchen	50000	5000000						3	0.255
2020-01-15T02:10:56	mnd9	kitchen	50000	5000000						3	0.255
2020-01-21T05:37:00	J.R. Allen	lapacer	50000	5000000						3	0.255
2020-01-27T15:29:17	mnd9	25836b	50000	5000000						3	0.255
2020-02-05T13:40:36	David_McCann	i5	50000	5000000						3	0.255
2020-02-13T06:16:30	mnd9	75201b	50000	5000000						3	0.255
2020-02-21T02:46:36	mnd9	libproj	50000	5000000						3	0.255
2020-02-27T02:40:26	Keysarecool	Boat_Anchor	50000	5000000						3	0.255
2020-03-05T05:24:04	mnd9	75201b	50000	5000000						3	0.255
2020-03-11T12:36:14	EricP	Cannonfodder	50000	5000000						3	0.255
2020-03-25T04:19:57	mnd9	25836b	50000	5000000						3	0.255
2020-03-30T22:12:27	mnd9	221Rb	50000	5000000						3	0.255
2020-04-13T07:36:37	nranks	wlaptop	50000	5000000						3	0.255
2020-04-23T23:40:31	mnd9	office2	50000	5000000						3	0.255
2020-05-01T07:26:10	daveward2005	Davy	50000	5000000						3	0.255
2020-05-13T03:25:39	nordi	sweet16	50000	5000000						3	0.255
2020-05-28T10:59:11	Keysarecool	HPLaptop	50000	5000000						3	0.255
2020-06-16T11:02:44	IanGlencross	glenx24	50000	5000000						3	0.255
2020-06-29T18:37:28	GAN	LMS-16	50000	5000000	41425672179242665817311	75.133	3	2	37721560204387	3	0.255

date	userid	compid	res64	spent (GHz-days)
2015-11-13T21:36:48	MadPoo	Manual testing	D7D3A888A3451B40	0.135

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 = 3600000, B2 = 180000000 (P-1 stage 2)

B1 = 2500000, B2 = 125000000 (P-1 stage 2)

B1 = 3600000 (P-1 stage 1)

B1 = 2500000 (P-1 stage 1)

B1 = 270000, B2 = 5832000 (P-1 stage 2)

B1 = 270000, B2 = 4860000 (P-1 stage 2)

B1 = 324000 (P-1 stage 1)

B1 = 135000, B2 = 2902500 (P-1 stage 2)

B1 = 270000 (P-1 stage 1)

B1 = 166241 (P-1 stage 1)

B1 = 135000 (P-1 stage 1)

B1 = 50000 (P-1 stage 1)

B1 = 20000, B2 = 280000 (P-1 stage 2)

B1 = 30000 (P-1 stage 1)

B1 = 20000 (P-1 stage 1)

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

B1 = 4000 (P-1 stage 1)

B1 = 2048 (P-1 stage 1)

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

10¹²

10¹³

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