M2542913 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	46.9488	68.1159%	3000000	135000000	1.0250	7.6206%	47.9739	70.5457%	2.4298%
PrimeNet	2⁵⁹	0.0302	62.7119%	11000	200000	0.0021	2.6839%	0.0323	63.7126%	1.0008%
GPU72	2⁶³	0.6276	65.0794%	12000	180000	0.0021	1.4772%	0.6298	65.5952%	0.5158%
Difference	+6	+46.3212	+3.0366%	+2988000	+134820000	+1.0229	+6.1434%	+47.3441	+4.9505%	+4.9505%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2542913	4181909840883774465563248441	28	91.756	822267580700514422940 2² × 3 × 5 × 23 × 4705577 × 126625506919	2021-07-09	4705577	126625506919	289,411,619	694.30	1,295.9

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2003-10-23T00:00:00	ANONYMOUS	v4_computers	2048	204800		-		-	-	0.001	-	-	0.190%
2003-11-08T00:00:00	Team Prime Rib	v4_computers	15000	198750		-		-	-	0.003	-	-	0.644%
2010-12-19T21:42:00	Jocelyn Larouche	Manual testing	20000	20000		-		-	-	0.002	-	-	0.222%
2011-01-02T14:09:00	Jocelyn Larouche	Manual testing	30000	30000		-		-	-	0.003	-	-	0.310%
2011-01-07T22:30:00	Jocelyn Larouche	Manual testing	50000	50000		-		-	-	0.005	-	-	0.454%
2011-02-28T09:55:00	James Heinrich	i7-920	300000	8000000		-		-	-	0.072	-	-	3.569%
2018-08-13T10:35:01	Jocelyn Larouche	low 4M	600000	6000000	6	-		-	-	0.090	-	-	3.663%
2018-09-15T22:47:02	mikr	MSI	3000000	135000000	12	-		-	-	1.025	-	-	7.621%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1999-03-26T00:00:00	Thomas Stork	v4_computers	2¹	2⁵⁹		-	-	0.030	-	-
2016-02-23T16:29:16	Mark Rose	Manual testing	2⁵⁹	2⁶⁰		-	-	0.030	-	-
2009-01-31T08:45:00	Sturle Sunde	aalto.ifi	2⁶⁰	2⁶¹		-	-	0.060	-	-
2012-06-15T12:43:00	Sebastian Hornbostel	Manual testing	2⁶¹	2⁶²		-	-	0.121	-	-
2013-11-10T05:46:00	lycorn	snail	2⁶²	2⁶³		-	-	0.386	-	-
2015-02-23T17:24:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.772	-	-
2015-02-23T17:24:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.469	-	-
2015-11-08T21:03:14	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	2.939	-	-
2017-08-08T13:42:10	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	5.877	-	-
2019-04-08T13:40:34	TJAOI	Manual testing	2⁶⁷	2⁶⁸		-	-	11.75	-	-
2021-06-21T08:54:18	TJAOI	Manual testing	2⁶⁸	2⁶⁹		-	-	23.51	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	11.451 GHz-days
Estimated T-Level:	22.214

Digits	B1	Curves	Complete	FacMiss
20	11000	124 / 100	1.240	28.758%
25	50000	124 / 280	0.443	64.169%

New Calculation Method

Total ECM effort:	11.451 GHz-days
Estimated T-Level:	22.214

Digits	B1	Complete	FacMiss
20	11000	4.772	0.846%
25	50000	0.442	64.291%
30	250000	0.028	97.252%
35	1000000	0.001	99.870%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		116	10.69
50000	5150000		7	0.653
50000	6750000	4181909840883774465563248441	1	0.106

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-02-13T21:23:00	Smurgs	Praca	50000	5000000						3	0.277
2010-04-29T01:58:00	unconnected	X3220--xp	50000	5000000						3	0.277
2012-09-26T18:22:00	Brian V.	dxl5420	50000	5000000						3	0.277
2014-03-28T16:59:00	Andy Incline	Office-PC	50000	5000000						3	0.277
2015-08-07T01:41:00	guru	w6	50000	5000000						3	0.277
2016-03-07T02:15:07	Jason U	Server7	50000	5000000						3	0.277
2016-07-17T15:26:43	lettp	Home	50000	5000000						3	0.277
2017-05-18T09:59:59	Ensigma	vps_sing	50000	5000000						3	0.277
2017-09-28T01:29:51	Chang Chia-Tche	ex-ctcpc	50000	5000000						3	0.277
2018-02-20T06:12:19	Chang Chia-Tche	ex-ctcpc	50000	5000000						3	0.277
2018-11-12T16:29:38	Chang Chia-Tche	ex-ctcpc	50000	5000000						3	0.277
2020-06-03T01:16:03	mnd9	25836b	50000	5000000						3	0.277
2020-06-27T07:41:40	S04803	lfmcal	50000	5000000						3	0.277
2020-07-01T12:37:16	GAN	LMS-02	50000	5000000						3	0.277
2020-07-08T04:59:47	GAN	LMS-13	50000	5000000						3	0.277
2020-07-14T07:22:45	GAN	LMS-17	50000	5000000						3	0.277
2020-07-26T02:40:45	mnd9	50871b	50000	5000000						3	0.277
2020-07-26T20:21:19	GAN	LMS-18	50000	5000000						3	0.277
2020-08-03T04:38:46	GAN	LMS-04	50000	5000000						3	0.277
2020-08-11T19:55:22	daveward2005	Dave2	50000	5000000						3	0.277
2020-08-27T00:15:22	M. R. Mayer	nimbus	50000	5000000						7	0.645
2020-09-29T17:14:46	mnd9	27016b	50000	5000000						7	0.645
2020-10-26T18:39:17	GAN	AC-KL	50000	5000000						7	0.645
2020-11-30T11:22:00	lycorn	colab_ES	50000	5000000						7	0.645
2021-01-09T00:04:43	mnd9	f4	50000	5000000						7	0.645
2021-02-02T22:16:31	Zenzoma	AMD3970X	50000	5000000						7	0.645
2021-03-03T11:58:31	Zenzoma	AM3700X_1	50000	5000000						7	0.645
2021-04-10T02:23:58	Brett Walker	brain	50000	5000000						7	0.645
2021-05-31T00:23:52	kutens	vega	50000	5150000						7	0.653
2021-07-09T16:25:23	kutens	terra	50000	6750000	4181909840883774465563248441	91.756	1	2	6310915476541309	1	0.106

date	userid	compid	res64	spent (GHz-days)
1999-04-23T00:00:00	ANONYMOUS	v4_computers	6F230284845A3EFB	0.176
2018-06-10T07:28:43	kkmrkkblmbrbk	old	6F230284845A3EFB	0.176

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 = 135000000 (P-1 stage 2)

B1 = 3000000 (P-1 stage 1)

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 = 198750 (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

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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