M2055679 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	28.9952	69.1176%	3600000	180000000	1.2595	8.5634%	30.2547	71.7622%	2.6446%
PrimeNet	2⁵⁸	0.0187	63.7931%	9000	160000	0.0016	2.6670%	0.0203	64.7587%	0.9656%
GPU72	2⁶²	0.2989	66.1290%	9000	120000	0.0014	1.3311%	0.3003	66.5799%	0.4508%
Difference	+6	+28.6964	+2.9886%	+3591000	+179880000	+1.2580	+7.2323%	+29.9544	+5.1823%	+5.1823%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2055679	49575296358145177499038727	26	85.358	12058131731205401597 7 × 43 × 239 × 167616059873023	2021-04-23	239	167616059873023	5,261,371	870,640	1,626,113

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%
2009-06-21T14:53:00	harlee	T7500_2200	20000	260000		-		-	-	0.003	-	-	0.873%
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%
2011-01-21T14:45:00	James Heinrich	i7-920	135000	2902500		-		-	-	0.027	-	-	2.716%
2014-10-26T00:59:00	Jocelyn Larouche	Manual testing	166223	166223		-		-	-	0.016	-	-	1.058%
2016-05-15T21:00:27	Jocelyn Larouche	Manual testing	270000	4860000	6	-		-	-	0.050	-	-	3.413%
2016-09-22T12:02:52	Jocelyn Larouche	low 4M	270000	5832000	6	-		-	-	0.055	-	-	3.551%
2016-11-07T03:11:23	Jocelyn Larouche	low 4M	324000	324000		-		-	-	0.031	-	-	1.482%
2017-02-02T09:34:40	mikr	MSI	2500000	125000000	12	-		-	-	0.875	-	-	7.882%
2017-03-13T15:12:12	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	-	-
2009-01-03T01:12:00	Sturle Sunde	gorky.ifi	2⁶⁰	2⁶¹		-	-	0.075	-	-
2012-03-11T19:47:00	Sebastian Hornbostel	Manual testing	2⁶¹	2⁶²		-	-	0.149	-	-
2013-09-01T20:20:00	ramgeis	Manual testing	2⁶²	2⁶³		-	-	0.478	-	-
2015-04-21T09:19:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.955	-	-
2015-04-21T09:19:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.818	-	-
2015-11-03T10:10:05	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	3.635	-	-
2016-08-18T20:55:12	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	7.270	-	-
2019-03-24T00:15:08	chuenkit	Manual testing	2⁶⁷	2⁶⁸		-	-	14.54	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	15.174 GHz-days
Estimated T-Level:	23.161

Digits	B1	Curves	Complete	FacMiss
20	11000	177 / 100	1.770	16.882%
25	50000	177 / 280	0.632	53.085%

New Calculation Method

Total ECM effort:	15.174 GHz-days
Estimated T-Level:	23.161

Digits	B1	Complete	FacMiss
20	11000	5.733	0.324%
25	50000	0.519	59.501%
30	250000	0.032	96.845%
35	1000000	0.001	99.853%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		172	14.60
50000	5000000	49575296358145177499038727	4	0.339
76620	23259610		1	0.238

ECM Details

										GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2008-12-08T03:13:00	paulie	iMac3.4	50000	5000000						3	0.255
2009-11-01T13:34:00	Conductor	home	50000	5000000						3	0.255
2011-04-15T19:09:00	James Hintz	ryan	50000	5000000						3	0.255
2013-03-12T11:25:00	OS1	L3	50000	5000000						3	0.255
2014-04-11T05:29:00	OS1	L3	50000	5000000						3	0.255
2015-07-13T05:01:00	guru	w6	50000	5000000						3	0.255
2016-02-19T22:29:39	Sintax	cloud	50000	5000000						3	0.255
2016-05-10T12:24:33	James P McMillan	caturday	50000	5000000						3	0.255
2016-07-18T01:00:19	Bruce	test	50000	5000000						3	0.255
2016-12-16T15:23:30	Bruce	Desk6	50000	5000000						3	0.255
2017-07-01T12:10:25	Bruce	Desk6	50000	5000000						3	0.255
2017-12-04T22:22:48	Lelikoid	QH	50000	5000000						3	0.255
2018-04-14T08:10:32	Bruce	Desk6	50000	5000000						3	0.255
2018-12-07T07:12:14	Section 31	vengeance	50000	5000000						3	0.255
2019-12-27T20:18:53	TheJudger	myECM	50000	5000000						3	0.255
2020-01-01T06:28:00	TheJudger	myECM	50000	5000000						3	0.255
2020-01-06T23:13:16	Nesowa	entropy_generator_2	50000	5000000						3	0.255
2020-01-15T10:31:26	mnd9	kitchen	50000	5000000						3	0.255
2020-01-21T11:25:14	mnd9	kitchen	50000	5000000						3	0.255
2020-01-28T13:00:10	mat10243x	C2	50000	5000000						3	0.255
2020-02-06T05:41:35	cappy95833	HomePC	50000	5000000						3	0.255
2020-02-13T08:24:34	Keysarecool	i9	50000	5000000						3	0.255
2020-02-20T16:54:51	EricP	Cannonfodder	50000	5000000						3	0.255
2020-02-27T10:29:51	daveward2005	Davy	50000	5000000						3	0.255
2020-03-05T08:50:18	Keysarecool	Boat_Anchor	50000	5000000						3	0.255
2020-03-12T05:56:03	mnd9	75201b	50000	5000000						3	0.255
2020-03-19T14:13:35	Keysarecool	HPLaptop	50000	5000000						3	0.255
2020-03-31T21:36:18	Sergey Nosov	TS140-02	50000	5000000						3	0.255
2020-04-13T17:34:47	Keysarecool	HPLaptop	50000	5000000						3	0.255
2020-04-24T15:06:57	Sergey Nosov	TS140-02	50000	5000000						3	0.255
2020-05-04T08:42:49	nordi	sweet16	50000	5000000						3	0.255
2020-05-13T07:19:04	EricP	Cannonfodder	50000	5000000						3	0.255
2020-05-29T17:05:34	daveward2005	Davy	50000	5000000						3	0.255
2020-06-20T00:12:21	Chang Chia-Tche	ex-ctcpc	50000	5000000						3	0.255
2020-06-29T19:35:05	GAN	LMS-02	50000	5000000						3	0.255
2020-07-06T19:21:21	GAN	LMS-04	50000	5000000						3	0.255
2020-07-14T02:22:16	Nesowa	entropy_generator_2	50000	5000000						3	0.255
2020-07-19T04:02:16	GAN	LMS-15	50000	5000000						3	0.255
2020-07-25T19:36:42	mnd9	kitchen	50000	5000000						3	0.255
2020-08-01T14:06:27	GAN	LMS-14	50000	5000000						3	0.255
2020-08-09T08:00:49	GAN	LMS-14	50000	5000000						3	0.255
2020-08-20T21:28:50	Nesowa	6700T	50000	5000000						7	0.594
2020-09-23T03:54:04	IanGlencross	glenx24	50000	5000000						7	0.594
2020-10-26T05:57:04	Brett Walker	brain	50000	5000000						7	0.594
2020-11-07T13:12:36	Bruno Victal	Manual testing	76620	23259610						1	0.238
2020-12-13T21:00:24	Zenzoma	AMD3970X	50000	5000000						7	0.594
2021-01-15T03:26:10	IanGlencross	glenx24	50000	5000000						7	0.594
2021-02-14T08:01:52	daveward2005	Dave2	50000	5000000						7	0.594
2021-03-14T22:03:10	Zenzoma	AMD3970X	50000	5000000						7	0.594
2021-04-23T09:10:57	daveward2005	Dave2	50000	5000000	49575296358145177499038727	85.358	4	2	7925941055475095	4	0.339

date	userid	compid	res64	spent (GHz-days)
2015-11-13T23:39:17	MadPoo	Manual testing	6F97CBE7A32C67__	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 = 166223 (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 = 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

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