M2605741 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	22.8744	67.6471%	3000000	90000000	0.7784	7.7809%	23.6529	70.1644%	2.5173%
PrimeNet	2⁵⁹	0.0295	62.7119%	11000	200000	0.0021	2.6960%	0.0316	63.7171%	1.0053%
GPU72	2⁶³	0.6125	65.0794%	12000	200000	0.0022	1.5310%	0.6147	65.6140%	0.5346%
Difference	+5	+22.2619	+2.5677%	+2988000	+89800000	+0.7762	+6.2499%	+23.0381	+4.5504%	+4.5504%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2605741	1745487219944986933447783	25	80.530	334931065663277151 3² × 11775461 × 3160348699	2020-07-30	11775461	3160348699	187,761	18.437	32.344

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2003-10-31T00:00:00	ANONYMOUS	v4_computers	2048	204800		-		-	-	0.001	-	-	0.238%
2003-11-08T00:00:00	Team Prime Rib	v4_computers	15000	217500		-		-	-	0.003	-	-	0.781%
2010-11-16T23:09:00	Jocelyn Larouche	Manual testing	20000	20000		-		-	-	0.002	-	-	0.266%
2010-12-16T03:52:00	markr	tiny	100000	2125000		-		-	-	0.021	-	-	2.472%
2014-10-10T20:28:00	Jocelyn Larouche	Manual testing	124632	124632		-		-	-	0.013	-	-	0.941%
2016-05-18T03:31:28	Jocelyn Larouche	Manual testing	200000	3600000	6	-		-	-	0.039	-	-	3.154%
2017-07-10T01:11:33	Jocelyn Larouche	low 4M	400000	4000000	6	-		-	-	0.060	-	-	3.544%
2019-12-03T14:18:33	masser	Manual testing	2000000	50000000	12	-		-	-	0.464	-	-	6.846%
2019-12-04T00:03:52	BigBrother	Winston	3000000	90000000	12	-		-	-	0.778	-	-	7.781%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1999-03-26T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁹		-	-	0.029	-	-
2016-02-23T16:29:17	Mark Rose	Manual testing	2⁵⁹	2⁶⁰		-	-	0.029	-	-
2009-01-27T16:57:00	Sturle Sunde	golan.ifi	2⁶⁰	2⁶¹		-	-	0.059	-	-
2012-06-24T10:42:00	Sebastian Hornbostel	Manual testing	2⁶¹	2⁶²		-	-	0.118	-	-
2013-01-14T11:55:00	dbaugh	Manual testing	2⁶²	2⁶³		-	-	0.377	-	-
2015-02-18T11:41:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.753	-	-
2015-02-18T11:41:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.434	-	-
2016-01-15T14:57:03	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	2.868	-	-
2017-08-24T10:53:49	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	5.736	-	-
2019-05-13T13:38:11	TJAOI	Manual testing	2⁶⁷	2⁶⁸		-	-	11.47	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	4.255 GHz-days
Estimated T-Level:	2.300

Digits	B1	Curves	Complete	FacMiss
20	11000	46 / 100	0.460	62.982%
25	50000	46 / 280	0.164	84.825%

New Calculation Method

Total ECM effort:	4.255 GHz-days
Estimated T-Level:	2.300

Digits	B1	Complete	FacMiss
20	11000	1.769	17.046%
25	50000	0.164	84.900%
30	250000	0.010	98.973%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		45	4.163
50000	5000000	1745487219944986933447783	1	0.093

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-02-24T03:36:00	Adel El-Atawy	LPTP	50000	5000000						3	0.278
2010-10-01T17:06:00	Lupo	yorick	50000	5000000						3	0.278
2012-11-17T17:11:00	Donna Noble	PH2x6	50000	5000000						3	0.278
2014-08-28T06:24:00	Lukasz Wrobel	i-1	50000	5000000						3	0.278
2015-10-17T06:15:07	lopper	i5-4670	50000	5000000						3	0.278
2016-03-22T09:35:30	Jason U	Server7	50000	5000000						3	0.278
2016-08-17T15:25:17	lettp	Home	50000	5000000						3	0.278
2017-06-09T00:45:48	Bruce	eleven	50000	5000000						3	0.278
2017-10-20T01:59:58	Chang Chia-Tche	ex-ctcpc	50000	5000000						3	0.278
2018-04-16T01:42:02	Chang Chia-Tche	ex-ctcpc	50000	5000000						3	0.278
2019-02-22T23:20:47	-Anonymous-		50000	5000000						3	0.278
2020-07-04T12:18:27	GAN	LMS-15	50000	5000000						3	0.278
2020-07-11T06:51:30	GAN	OSK-01	50000	5000000						3	0.278
2020-07-16T23:12:13	GAN	LMS-18	50000	5000000						3	0.278
2020-07-23T03:11:59	Nesowa	6700T	50000	5000000						3	0.278
2020-07-30T09:29:40	rextherunt	ice	50000	5000000	1745487219944986933447783	80.530	1	2		1	0.093

date	userid	compid	res64	spent (GHz-days)
1999-03-26T00:00:00	ANONYMOUS	v4_computers	9D871527A8643DE4	0.181
2018-06-27T22:02:15	kkmrkkblmbrbk	old	9D871527A8643DE4	0.181

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 = 90000000 (P-1 stage 2)

B1 = 2000000, B2 = 50000000 (P-1 stage 2)

B1 = 3000000 (P-1 stage 1)

B1 = 2000000 (P-1 stage 1)

B1 = 400000, B2 = 4000000 (P-1 stage 2)

B1 = 400000 (P-1 stage 1)

B1 = 200000, B2 = 3600000 (P-1 stage 2)

B1 = 100000, B2 = 2125000 (P-1 stage 2)

B1 = 200000 (P-1 stage 1)

B1 = 124632 (P-1 stage 1)

B1 = 100000 (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)

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

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