M2359043 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	25.2665	67.6471%	3000000	100000000	0.8115	7.8334%	26.0781	70.1814%	2.5343%
PrimeNet	2⁵⁸	0.0163	62.0690%	11000	200000	0.0021	3.0508%	0.0184	63.2262%	1.1572%
GPU72	2⁶²	0.2604	64.5161%	13000	220000	0.0024	1.8369%	0.2628	65.1679%	0.6518%
Difference	+6	+25.0061	+3.1309%	+2987000	+99780000	+0.8092	+5.9965%	+25.8153	+5.0135%	+5.0135%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2359043	1168252106314184884777	22	69.985	247611448013916 2² × 3 × 7 × 2947755333499	2020-04-29	7	2947755333499	58.902	15,732	29,383

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2003-09-21T00:00:00	ANONYMOUS	v4_computers	2048	204800		-		-	-	0.001	-	-	0.231%
2010-11-03T21:25:00	Jocelyn Larouche	Manual testing	20000	20000		-		-	-	0.002	-	-	0.260%
2010-12-22T21:22:00	Oscar Östlin		75011	75011		-		-	-	0.007	-	-	0.682%
2011-01-23T13:57:00	Oscar Östlin		90000	1822500		-		-	-	0.018	-	-	2.297%
2014-08-07T10:52:00	Jocelyn Larouche	Manual testing	117208	117208		-		-	-	0.011	-	-	0.893%
2014-10-22T23:53:00	Jocelyn Larouche	Manual testing	144416	144416		-		-	-	0.014	-	-	1.004%
2015-08-15T23:31:00	mikr	MSI	3000000	100000000		-		-	-	0.812	-	-	7.833%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2016-02-23T16:29:12	Mark Rose	Manual testing	2¹	2⁶⁰		-	-	0.065	-	-
2009-01-17T11:12:00	Sturle Sunde	kraus.ifi	2⁶⁰	2⁶¹		-	-	0.065	-	-
2012-05-30T07:42:00	Sebastian Hornbostel	Manual testing	2⁶¹	2⁶²		-	-	0.130	-	-
2013-12-04T21:14:00	Jerry Hallett	Manual testing	2⁶²	2⁶³		-	-	0.416	-	-
2015-03-06T11:15:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.832	-	-
2015-03-06T11:15:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.584	-	-
2015-10-29T11:36:25	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	3.168	-	-
2017-06-13T16:34:54	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	6.335	-	-
2019-04-22T13:11:35	TJAOI	Manual testing	2⁶⁷	2⁶⁸		-	-	12.67	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	4.529 GHz-days
Estimated T-Level:	2.550

Digits	B1	Curves	Complete	FacMiss
20	11000	51 / 100	0.510	59.896%
25	50000	51 / 280	0.182	83.321%

New Calculation Method

Total ECM effort:	4.529 GHz-days
Estimated T-Level:	2.550

Digits	B1	Complete	FacMiss
20	11000	1.645	19.298%
25	50000	0.149	86.184%
30	250000	0.009	99.089%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		48	4.262
50000	5000000	1168252106314184884777	3	0.266

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-01-28T15:21:00	Never Odd Or Even	T_Quad	50000	5000000						3	0.266
2010-02-02T14:11:00	James Classen	towerofart	50000	5000000						3	0.266
2012-01-02T20:00:00	S36049	Wolle5	50000	5000000						3	0.266
2013-11-01T09:59:00	arnaud	srv-630	50000	5000000						3	0.266
2015-06-13T15:42:00	guru	w6	50000	5000000						3	0.266
2016-02-17T14:29:42	Sintax	cloud2	50000	5000000						3	0.266
2016-05-12T06:22:31	Bruce	Desk6	50000	5000000						3	0.266
2016-09-02T17:16:05	Bruce	Desk6	50000	5000000						3	0.266
2017-03-05T15:28:43	Bruce	Desk6	50000	5000000						3	0.266
2017-10-12T03:41:40	Bruce	Desk6	50000	5000000						3	0.266
2018-03-03T22:55:56	Bruce	Desk6	50000	5000000						3	0.266
2018-09-03T14:53:57	Bruce	Desk6	50000	5000000						3	0.266
2020-03-17T20:44:01	MarkS	desktop-i7	50000	5000000						3	0.266
2020-03-28T08:08:43	EricP	Cannonfodder	50000	5000000						3	0.266
2020-04-09T22:19:28	mnd9	libproj	50000	5000000						3	0.266
2020-04-22T12:12:17	nordi	sweet16	50000	5000000						3	0.266
2020-04-29T21:41:11	Keysarecool	Boat_Anchor	50000	5000000	1168252106314184884777	69.985	3	2	3171388632193773	3	0.266

date	userid	compid	res64	spent (GHz-days)
1999-03-15T00:00:00	ANONYMOUS	v4_computers	EA3409518D6757FF	0.159
2018-05-10T18:43:38	kkmrkkblmbrbk	old	EA3409518D6757FF	0.159

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 = 3000000, B2 = 100000000 (P-1 stage 2)

B1 = 3000000 (P-1 stage 1)

B1 = 90000, B2 = 1822500 (P-1 stage 2)

B1 = 144416 (P-1 stage 1)

B1 = 117208 (P-1 stage 1)

B1 = 90000 (P-1 stage 1)

B1 = 75011 (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

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