M2704193 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	22.0417	67.6471%	600000	6000000	0.1001	4.0794%	22.1418	68.9669%	1.3198%
PrimeNet	2⁵⁹	0.0284	62.7119%	12000	220000	0.0026	2.8438%	0.0310	63.7723%	1.0604%
GPU72	2⁶³	0.5902	65.0794%	14000	220000	0.0028	1.6618%	0.5930	65.6597%	0.5803%
Difference	+5	+21.4514	+2.5677%	+586000	+5780000	+0.0973	+2.4176%	+21.5488	+3.3072%	+3.3072%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2704193	430419991606264251284911	24	78.510	79583815135654935 3 × 5 × 7 × 757941096530047	2020-10-29	7	757941096530047	34,471	4,624,693	8,637,639

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2003-11-08T00:00:00	ANONYMOUS	v4_computers	2048	204800		-		-	-	0.001	-	-	0.240%
2003-11-28T00:00:00	Team Prime Rib	v4_computers	15000	217500		-		-	-	0.003	-	-	0.787%
2010-12-16T22:40:00	Jocelyn Larouche	Manual testing	20000	20000		-		-	-	0.002	-	-	0.268%
2010-12-26T14:29:00	Jocelyn Larouche	Manual testing	30000	30000		-		-	-	0.003	-	-	0.371%
2011-01-18T00:04:00	Jocelyn Larouche	Manual testing	50000	50000		-		-	-	0.006	-	-	0.537%
2011-03-20T07:37:00	James Heinrich	WHS	300000	8000000		-		-	-	0.081	-	-	3.990%
2018-07-23T01:07:55	Jocelyn Larouche	low 4M	600000	6000000	6	-		-	-	0.100	-	-	4.079%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2016-02-23T16:29:19	Mark Rose	Manual testing	2¹	2⁶⁰		-	-	0.057	-	-
2009-01-31T02:38:00	Sturle Sunde	hummel.ifi	2⁶⁰	2⁶¹		-	-	0.057	-	-
2012-05-06T05:06:00	Grant McCracken	thumper	2⁶¹	2⁶²		-	-	0.114	-	-
2013-01-10T10:18:00	dbaugh	Manual testing	2⁶²	2⁶³		-	-	0.363	-	-
2015-04-13T20:09:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.726	-	-
2015-04-13T20:09:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.382	-	-
2016-01-29T11:11:44	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	2.763	-	-
2017-09-29T00:40:42	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	5.527	-	-
2019-02-11T01:15:27	chuenkit	Manual testing	2⁶⁷	2⁶⁸		-	-	11.05	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	6.320 GHz-days
Estimated T-Level:	3.050

Digits	B1	Curves	Complete	FacMiss
20	11000	61 / 100	0.610	54.169%
25	50000	61 / 280	0.218	80.393%

New Calculation Method

Total ECM effort:	6.320 GHz-days
Estimated T-Level:	3.050

Digits	B1	Complete	FacMiss
20	11000	1.968	13.977%
25	50000	0.178	83.707%
30	250000	0.011	98.911%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		56	5.802
50000	5000000	430419991606264251284911	5	0.518

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-03-13T16:17:00	bayanne	MacBook	50000	5000000						3	0.311
2010-08-14T22:39:00	Wolfgang Fluck	C91F72025	50000	5000000						3	0.311
2013-01-15T22:32:00	Brian V.	dxl5420	50000	5000000						3	0.311
2015-02-22T09:31:00	S36049	Wolle5	50000	5000000						3	0.311
2016-02-02T22:10:13	Bruce	Desk8	50000	5000000						3	0.311
2016-04-30T13:29:31	lettp	Home	50000	5000000						3	0.311
2016-11-08T15:05:27	S36049	Wolle5	50000	5000000						3	0.311
2017-07-13T17:04:29	Bruce	eleven	50000	5000000						3	0.311
2017-11-26T10:24:46	Yan Jinzhao	cndns	50000	5000000						3	0.311
2018-07-03T08:17:04	Chang Chia-Tche	ex-ctcpc	50000	5000000						3	0.311
2019-10-12T01:24:21	Chang Chia-Tche	ex-ctcpc	50000	5000000						3	0.311
2020-07-27T19:18:26	GAN	LMS-03	50000	5000000						3	0.311
2020-08-04T04:21:28	GAN	LMS-16	50000	5000000						3	0.311
2020-08-12T02:59:31	GAN	LMS-03	50000	5000000						3	0.311
2020-09-01T17:00:33	mnd9	75203b	50000	5000000						7	0.725
2020-10-03T15:59:01	lycorn	colab_S	50000	5000000						7	0.725
2020-10-29T09:35:13	mnd9	75204	50000	5000000	430419991606264251284911	78.510	5	2	8808958297347993	5	0.518

date	userid	compid	res64	spent (GHz-days)
1999-05-02T00:00:00	ANONYMOUS	v4_computers	EB2042F2A140DD5C	0.209
2018-07-31T18:23:06	kkmrkkblmbrbk	old	EB2042F2A140DD5C	0.209

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 = 600000, B2 = 6000000 (P-1 stage 2)

B1 = 300000, B2 = 8000000 (P-1 stage 2)

B1 = 600000 (P-1 stage 1)

B1 = 300000 (P-1 stage 1)

B1 = 50000 (P-1 stage 1)

B1 = 30000 (P-1 stage 1)

B1 = 15000, B2 = 217500 (P-1 stage 2)

B1 = 20000 (P-1 stage 1)

B1 = 15000 (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

10⁰

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10²

10³

10⁴

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10⁶

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10⁸

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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