M2075833 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	57.5127	69.5652%	4000000	200000000	1.3994	8.1084%	58.9121	72.0330%	2.4678%
PrimeNet	2⁵⁸	0.0185	63.7931%	9000	160000	0.0016	2.6719%	0.0201	64.7605%	0.9674%
GPU72	2⁶²	0.2960	66.1290%	9000	130000	0.0015	1.3672%	0.2974	66.5921%	0.4631%
Difference	+7	+57.2168	+3.4362%	+3991000	+199870000	+1.3979	+6.7413%	+58.6147	+5.4409%	+5.4409%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2075833	3940167732016334942303	22	71.739	949057012779047 949057012779047	2021-10-05	1	949057012779047	373.28	4,929,639	9,207,194

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2003-02-27T00:00:00	ANONYMOUS	v4_computers	2048	204800		-		-	-	0.001	-	-	0.179%
2009-07-25T10:51:00	harlee	P4_2600	20000	260000		-		-	-	0.003	-	-	0.751%
2010-12-28T02:15:00	Jocelyn Larouche	Manual testing	30000	30000		-		-	-	0.003	-	-	0.296%
2011-01-07T22:30:00	Jocelyn Larouche	Manual testing	50000	50000		-		-	-	0.005	-	-	0.435%
2011-01-20T18:42:00	James Heinrich	Q6600	135000	3071250		-		-	-	0.028	-	-	2.455%
2014-11-10T23:29:00	Jocelyn Larouche	Manual testing	165920	165920		-		-	-	0.016	-	-	0.925%
2015-01-29T22:02:00	Jocelyn Larouche	Manual testing	207400	207400		-		-	-	0.020	-	-	1.044%
2015-01-30T21:42:00	Jocelyn Larouche	Manual testing	228140	228140		-		-	-	0.022	-	-	1.098%
2015-01-31T14:55:00	Jocelyn Larouche	Manual testing	250954	250954		-		-	-	0.024	-	-	1.153%
2015-02-11T12:22:00	Jocelyn Larouche	Manual testing	404160	404160		-		-	-	0.039	-	-	1.456%
2015-02-14T12:30:00	Jocelyn Larouche	Manual testing	537936	537936		-		-	-	0.051	-	-	1.659%
2015-02-16T20:56:00	Jocelyn Larouche	Manual testing	591729	591729		-		-	-	0.056	-	-	1.730%
2015-02-25T03:47:00	Jocelyn Larouche	Manual testing	650901	650901		-		-	-	0.062	-	-	1.802%
2015-03-03T20:46:00	Jocelyn Larouche	Manual testing	715991	715991		-		-	-	0.068	-	-	1.877%
2015-03-12T10:39:00	Jocelyn Larouche	Manual testing	787590	787590		-		-	-	0.075	-	-	1.953%
2015-03-15T18:55:00	Jocelyn Larouche	Manual testing	866349	866349		-		-	-	0.083	-	-	2.031%
2015-04-08T16:59:00	Jocelyn Larouche	Manual testing	1048281	1048281		-		-	-	0.100	-	-	2.192%
2015-05-01T17:21:00	Jocelyn Larouche	Manual testing	1268419	1268419		-		-	-	0.121	-	-	2.360%
2015-05-07T16:19:00	Jocelyn Larouche	Manual testing	1395260	1395260		-		-	-	0.133	-	-	2.446%
2015-05-22T00:29:00	Jocelyn Larouche	Manual testing	1534786	1534786		-		-	-	0.146	-	-	2.535%
2015-05-26T18:17:00	Jocelyn Larouche	Manual testing	1688264	1688264		-		-	-	0.161	-	-	2.624%
2015-06-08T13:43:00	Jocelyn Larouche	Manual testing	1857090	1857090		-		-	-	0.177	-	-	2.716%
2015-06-25T21:15:00	Jocelyn Larouche	Manual testing	2042799	2042799		-		-	-	0.195	-	-	2.809%
2015-07-07T18:13:00	Jocelyn Larouche	Manual testing	2247078	2247078		-		-	-	0.214	-	-	2.905%
2016-07-07T00:37:33	Jocelyn Larouche	Manual testing	2247078	4494156	6	-		-	-	0.226	-	-	3.626%
2016-09-24T23:31:24	Jocelyn Larouche	low 4M	2247078	8988312	6	-		-	-	0.249	-	-	4.354%
2018-02-23T11:35:54	Jocelyn Larouche	low 4M	2257078	4514156	6	-		-	-	0.227	-	-	3.631%
2018-09-28T10:10:34	Jocelyn Larouche	low 4M	2257078	20758330	12	-		-	-	0.311	-	-	5.246%
2019-09-10T06:33:08	mikr	MSI	4000000	200000000	12	-		-	-	1.399	-	-	8.108%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1999-01-10T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.018	-	-
2016-02-23T16:29:04	Mark Rose	Manual testing	2⁵⁸	2⁶⁰		-	-	0.055	-	-
2009-01-03T04:00:00	Sturle Sunde	homilius.ifi	2⁶⁰	2⁶¹		-	-	0.074	-	-
2012-03-16T19:47:00	Sebastian Hornbostel	Manual testing	2⁶¹	2⁶²		-	-	0.148	-	-
2013-09-01T20:21:00	ramgeis	Manual testing	2⁶²	2⁶³		-	-	0.473	-	-
2015-03-28T18:03:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.946	-	-
2015-03-28T18:03:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.800	-	-
2015-10-21T19:11:16	omylist	Manual testing	2⁶⁵	2⁶⁶		-	-	3.600	-	-
2016-09-10T20:44:41	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	7.200	-	-
2019-03-29T01:44:37	chuenkit	Manual testing	2⁶⁷	2⁶⁸		-	-	14.40	-	-
2021-07-29T11:14:33	TJAOI	Manual testing	2⁶⁸	2⁶⁹		-	-	28.80	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	17.069 GHz-days
Estimated T-Level:	23.536

Digits	B1	Curves	Complete	FacMiss
20	11000	198 / 100	1.980	13.670%
25	50000	198 / 280	0.707	49.243%

New Calculation Method

Total ECM effort:	17.069 GHz-days
Estimated T-Level:	23.536

Digits	B1	Complete	FacMiss
20	11000	6.426	0.162%
25	50000	0.582	55.866%
30	250000	0.036	96.469%
35	1000000	0.002	99.835%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		183	15.55
50000	5000000	3940167732016334942303	7	0.595
50000	6750000		7	0.680
76620	24176890		1	0.244

ECM Details

										GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2008-12-12T20:43:00	Luigi Morelli	AMD64x2	50000	5000000						3	0.255
2009-10-29T15:31:00	gumbald	jimbo	50000	5000000						3	0.255
2011-05-04T21:34:00	James Hintz	ryan	50000	5000000						3	0.255
2013-03-15T15:26:00	Donna Noble	opt4820	50000	5000000						3	0.255
2014-08-10T08:32:00	he4var		50000	5000000						3	0.255
2015-07-23T11:03:00	guru	w6	50000	5000000						3	0.255
2016-02-20T13:16:02	Sintax	cloud	50000	5000000						3	0.255
2016-05-14T18:23:12	lettp	Home	50000	5000000						3	0.255
2016-07-24T15:14:04	Bruce	test	50000	5000000						3	0.255
2017-01-05T20:11:50	Bruce	Desk6	50000	5000000						3	0.255
2017-07-23T21:10:18	Bruce	Desk6	50000	5000000						3	0.255
2017-12-18T09:06:30	Bruce	Desk6	50000	5000000						3	0.255
2018-05-09T04:16:47	Bruce	Desk6	50000	5000000						3	0.255
2018-10-12T16:32:07	storm5510	7700_Kaby_Lake	50000	5000000						3	0.255
2020-01-01T10:45:04	J.R. Allen	lapacer	50000	5000000						3	0.255
2020-01-07T08:47:30	daveward2005	MW	50000	5000000						3	0.255
2020-01-15T10:20:03	daveward2005	MW	50000	5000000						3	0.255
2020-01-21T13:35:38	David_McCann	i5	50000	5000000						3	0.255
2020-01-27T21:42:40	mnd9	25836b	50000	5000000						3	0.255
2020-02-06T01:35:10	cappy95833	HomePC	50000	5000000						3	0.255
2020-02-13T11:35:17	mnd9	75201b	50000	5000000						3	0.255
2020-02-20T13:48:11	Keysarecool	HPLaptop	50000	5000000						3	0.255
2020-02-27T06:55:53	kracker	O0	50000	5000000						3	0.255
2020-03-05T03:10:39	MarkS	laptop64	50000	5000000						3	0.255
2020-03-12T05:56:44	mnd9	25836b	50000	5000000						3	0.255
2020-03-31T11:40:36	nordi	sweet16	50000	5000000						3	0.255
2020-04-13T06:14:29	EricP	Cannonfodder	50000	5000000						3	0.255
2020-04-24T02:51:24	Keysarecool	HPLaptop	50000	5000000						3	0.255
2020-05-12T01:35:19	mnd9	75211backdoorb	50000	5000000						3	0.255
2020-05-13T11:53:42	nordi	sweet16	50000	5000000						3	0.255
2020-05-19T15:04:39	Sergey Nosov	TS140-02	50000	5000000						3	0.255
2020-05-29T13:35:33	Leo Custodio	G1-PRIME96-01	50000	5000000						3	0.255
2020-06-16T19:34:11	GAN	PG-HP	50000	5000000						3	0.255
2020-06-29T17:16:18	GAN	OSB-01	50000	5000000						3	0.255
2020-07-06T14:37:02	GAN	LMS-13	50000	5000000						3	0.255
2020-07-12T23:33:00	GAN	LMS-17	50000	5000000						3	0.255
2020-07-19T00:14:24	GAN	PG-HP	50000	5000000						3	0.255
2020-07-25T04:55:28	GAN	LMS-02	50000	5000000						3	0.255
2020-08-01T08:31:02	GAN	PG-HP	50000	5000000						3	0.255
2020-08-09T15:08:22	Leo Custodio	G1-PRIME96-01	50000	5000000						3	0.255
2020-08-22T18:33:29	LaurV	debilis	50000	5000000						7	0.595
2020-09-22T05:32:51	mnd9	50871b	50000	5000000						7	0.595
2020-10-20T08:16:00	Albrecht Heeffer	R7-3800X	50000	5000000						7	0.595
2020-11-09T21:37:20	Bruno Victal	Manual testing	76620	24176890						1	0.244
2020-12-13T05:53:10	Zenzoma	AMD3970X	50000	5000000						7	0.595
2021-01-07T02:47:24	Cork	Manual testing	50000	5000000						7	0.595
2021-02-13T14:42:08	mnd9	l2lounge	50000	5000000						7	0.595
2021-03-14T18:55:01	daveward2005	Dave2	50000	5000000						7	0.595
2021-04-23T00:56:39	IanGlencross	glenx24	50000	5000000						7	0.595
2021-06-12T21:15:19	GAN	KL-SCH04	50000	5000000						7	0.595
2021-07-23T08:27:00	kutens	terra	50000	6750000						7	0.680
2021-10-05T23:29:26	GAN	KL-SCH09	50000	5000000	3940167732016334942303	71.739	7	2	3995419300442220	7	0.595

date	userid	compid	res64	spent (GHz-days)
1999-01-29T00:00:00	ANONYMOUS	v4_computers	7199C4DC8422DBD2	0.136
2017-05-31T01:25:33	kkmrkkblmbrbk	c4.large	7199C4DC8422DBD2	0.136

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 = 4000000, B2 = 200000000 (P-1 stage 2)

B1 = 4000000 (P-1 stage 1)

B1 = 2257078, B2 = 20758330 (P-1 stage 2)

B1 = 2247078, B2 = 8988312 (P-1 stage 2)

B1 = 2257078, B2 = 4514156 (P-1 stage 2)

B1 = 2247078, B2 = 4494156 (P-1 stage 2)

B1 = 2257078 (P-1 stage 1)

B1 = 2247078 (P-1 stage 1)

B1 = 2042799 (P-1 stage 1)

B1 = 1857090 (P-1 stage 1)

B1 = 1688264 (P-1 stage 1)

B1 = 1534786 (P-1 stage 1)

B1 = 1395260 (P-1 stage 1)

B1 = 1268419 (P-1 stage 1)

B1 = 1048281 (P-1 stage 1)

B1 = 866349 (P-1 stage 1)

B1 = 787590 (P-1 stage 1)

B1 = 715991 (P-1 stage 1)

B1 = 650901 (P-1 stage 1)

B1 = 591729 (P-1 stage 1)

B1 = 537936 (P-1 stage 1)

B1 = 404160 (P-1 stage 1)

B1 = 135000, B2 = 3071250 (P-1 stage 2)

B1 = 250954 (P-1 stage 1)

B1 = 228140 (P-1 stage 1)

B1 = 207400 (P-1 stage 1)

B1 = 165920 (P-1 stage 1)

B1 = 135000 (P-1 stage 1)

B1 = 50000 (P-1 stage 1)

B1 = 20000, B2 = 260000 (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 = 2048 (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

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