M2819491 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	2⁷⁰	84.7496	68.5714%	5000000	200000000	1.7498	7.8484%	86.4993	71.0381%	2.4666%
PrimeNet	2⁵⁹	0.0272	62.7119%	12000	240000	0.0027	2.9308%	0.0300	63.8047%	1.0928%
GPU72	2⁶³	0.5661	65.0794%	15000	260000	0.0032	1.7921%	0.5692	65.7052%	0.6258%
Difference	+7	+84.1835	+3.4921%	+4985000	+199740000	+1.7466	+6.0563%	+85.9301	+5.3329%	+5.3329%

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2003-11-28T00:00:00	ANONYMOUS	v4_computers	2048	204800		-		-	-	0.001	-	-	0.158%
2016-09-11T16:07:10	Jocelyn Larouche	low 4M	160000	3300000	6	-		-	-	0.037	-	-	2.404%
2016-12-19T18:37:54	Jocelyn Larouche	low 4M	192000	192000		-		-	-	0.022	-	-	0.925%
2017-01-10T10:25:16	Jocelyn Larouche	low 4M	230400	230400		-		-	-	0.026	-	-	1.020%
2017-04-04T20:17:34	Jocelyn Larouche	low 4M	331776	3317760	6	-		-	-	0.055	-	-	2.707%
2018-09-03T21:22:22	Jocelyn Larouche	low 4M	506131	506131		-		-	-	0.057	-	-	1.502%
2018-09-05T22:38:03	Jocelyn Larouche	low 4M	607357	607357		-		-	-	0.068	-	-	1.629%
2018-09-12T23:00:20	Jocelyn Larouche	low 4M	663552	1327104	4	-		-	-	0.078	-	-	2.217%
2019-05-22T10:32:22	BigBrother	Winston	1000000	10000000	12	-		-	-	0.167	-	-	3.970%
2019-11-10T16:24:59	masser	Manual testing	3000000	30000000	12	-		-	-	0.501	-	-	5.454%
2020-01-19T15:04:42	masser	Manual testing	5000000	200000000	12	-		-	-	1.750	-	-	7.848%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2016-02-23T16:29:22	Mark Rose	Manual testing	2¹	2⁶⁰		-	-	0.054	-	-
2009-02-13T20:05:00	Sturle Sunde	fizir.ifi	2⁶⁰	2⁶¹		-	-	0.054	-	-
2012-02-24T07:39:00	Grant McCracken	thumper	2⁶¹	2⁶²		-	-	0.109	-	-
2013-01-10T10:21:00	dbaugh	Manual testing	2⁶²	2⁶³		-	-	0.348	-	-
2015-04-21T09:19:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.696	-	-
2015-04-21T09:19:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.325	-	-
2016-02-12T10:12:11	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	2.650	-	-
2017-10-28T16:39:37	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	5.301	-	-
2017-11-06T09:42:44	mikr	Manual testing	2⁶⁷	2⁶⁸		-	-	10.60	-	-
2018-05-15T16:09:47	Yxinity	Manual testing	2⁶⁸	2⁶⁹		-	-	21.20	-	-
2018-05-15T16:09:47	Yxinity	Manual testing	2⁶⁹	2⁷⁰		-	-	42.41	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	12.712 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:	12.712 GHz-days
Estimated T-Level:	22.161

Digits	B1	Complete	FacMiss
20	11000	4.676	0.931%
25	50000	0.432	64.901%
30	250000	0.027	97.309%
35	1000000	0.001	99.873%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		114	11.89
50000	6450000		7	0.822

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-03-24T08:24:00	Newro	home	50000	5000000						3	0.313
2010-10-26T06:37:00	James Hintz	ryan	50000	5000000						3	0.313
2013-03-30T19:56:00	Donna Noble	PH2x6	50000	5000000						3	0.313
2015-03-28T22:56:00	Bruce	desk16	50000	5000000						3	0.313
2016-02-18T02:05:29	Sintax	cloud	50000	5000000						3	0.313
2016-06-06T12:09:56	Jason U	Server7	50000	5000000						3	0.313
2017-02-22T00:21:37	Bruce	eleven	50000	5000000						3	0.313
2017-09-01T18:43:49	Chang Chia-Tche	ex-ctcpc	50000	5000000						3	0.313
2018-02-23T11:53:22	Chang Chia-Tche	ex-ctcpc	50000	5000000						3	0.313
2019-01-10T08:24:09	Palantsevich	OfficeB01	50000	5000000						3	0.313
2020-09-04T10:28:48	GAN	KA-HP	50000	5000000						7	0.730
2020-10-07T02:22:11	IanGlencross	glenx24	50000	5000000						7	0.730
2020-11-03T10:09:11	mnd9	kitchen	50000	5000000						7	0.730
2020-12-08T12:29:02	Zenzoma	AMD3970X	50000	5000000						7	0.730
2021-01-11T20:41:51	daveward2005	MW	50000	5000000						7	0.730
2021-02-11T06:40:19	Massimo Cappelli (ik5pwa)	maxwinxp_1	50000	5000000						7	0.730
2021-03-10T12:38:38	Zenzoma	AMD3970X	50000	5000000						7	0.730
2021-04-20T17:33:22	GAN	KL-SCH09	50000	5000000						7	0.730
2021-06-10T00:47:44	Sergey Nosov	TS140-02	50000	5000000						7	0.730
2021-07-19T03:08:04	kutens	canopus	50000	6450000						7	0.822
2021-09-18T18:13:26	MarkS	desktop-i7	50000	5000000						7	0.730
2021-12-11T07:13:45	daveward2005	d12436	50000	5000000						7	0.730
2022-06-05T07:18:20	Claude Portenier	Petit-Idiot	50000	5000000						7	0.730

date	userid	compid	res64	spent (GHz-days)
1999-05-30T00:00:00	ANONYMOUS	v4_computers	7F84301A2CC582C2	0.218
2018-09-06T18:00:30	kkmrkkblmbrbk	old	7F84301A2CC582C2	0.218

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 = 5000000, B2 = 200000000 (P-1 stage 2)

B1 = 5000000 (P-1 stage 1)

B1 = 3000000, B2 = 30000000 (P-1 stage 2)

B1 = 3000000 (P-1 stage 1)

B1 = 1000000, B2 = 10000000 (P-1 stage 2)

B1 = 1000000 (P-1 stage 1)

B1 = 663552, B2 = 1327104 (P-1 stage 2)

B1 = 663552 (P-1 stage 1)

B1 = 607357 (P-1 stage 1)

B1 = 506131 (P-1 stage 1)

B1 = 331776, B2 = 3317760 (P-1 stage 2)

B1 = 331776 (P-1 stage 1)

B1 = 160000, B2 = 3300000 (P-1 stage 2)

B1 = 230400 (P-1 stage 1)

B1 = 192000 (P-1 stage 1)

B1 = 160000 (P-1 stage 1)

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

B1 = 2048 (P-1 stage 1)

10²

10³

10⁴

10⁵

10⁶

10⁷

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

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