M2453573 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	48.6583	68.1159%	3730000	414030000	2.6234	9.0674%	51.2817	71.0070%	2.8911%
PrimeNet	2⁵⁹	0.0313	62.7119%	10000	180000	0.0019	2.5290%	0.0332	63.6549%	0.9430%
GPU72	2⁶³	0.6505	65.0794%	10000	160000	0.0018	1.3337%	0.6523	65.5451%	0.4658%
Difference	+6	+48.0079	+3.0366%	+3720000	+413870000	+2.6216	+7.7336%	+50.6294	+5.4619%	+5.4619%

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2003-10-14T00:00:00	ANONYMOUS	v4_computers	2048	204800		-		-	-	0.001	-	-	0.188%
2003-10-31T00:00:00	Team Prime Rib	v4_computers	15000	232500		-		-	-	0.003	-	-	0.672%
2010-12-22T11:37:00	Jocelyn Larouche	Manual testing	20000	20000		-		-	-	0.002	-	-	0.220%
2011-01-19T21:08:00	Oscar Östlin		95000	1947500		-		-	-	0.020	-	-	2.104%
2014-02-09T05:17:00	mikr	MSI	3102822	43439508		-		-	-	0.533	-	-	6.299%
2021-06-17T00:27:15	Dylan Delgado	laptop-ryzen73700	3730000	414030000		-		-	-	2.623	-	-	9.067%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1999-08-07T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁹		-	-	0.031	-	-
2016-02-23T16:29:14	Mark Rose	Manual testing	2⁵⁹	2⁶⁰		-	-	0.031	-	-
2009-01-15T20:08:00	Sturle Sunde	czerny.ifi	2⁶⁰	2⁶¹		-	-	0.063	-	-
2012-06-07T11:43:00	Sebastian Hornbostel	Manual testing	2⁶¹	2⁶²		-	-	0.125	-	-
2013-12-04T21:13:00	Jerry Hallett	Manual testing	2⁶²	2⁶³		-	-	0.400	-	-
2015-03-03T21:37:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.800	-	-
2015-03-03T21:37:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.523	-	-
2015-10-25T20:35:05	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	3.046	-	-
2017-07-14T10:08:13	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	6.091	-	-
2019-07-17T09:51:52	TJAOI	Manual testing	2⁶⁷	2⁶⁸		-	-	12.18	-	-
2021-06-03T11:40:09	TJAOI	Manual testing	2⁶⁸	2⁶⁹		-	-	24.37	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	15.532 GHz-days
Estimated T-Level:	22.911

Digits	B1	Curves	Complete	FacMiss
20	11000	163 / 100	1.630	19.433%
25	50000	163 / 280	0.582	55.812%

New Calculation Method

Total ECM effort:	15.532 GHz-days
Estimated T-Level:	22.911

Digits	B1	Complete	FacMiss
20	11000	6.356	0.174%
25	50000	0.587	55.583%
30	250000	0.037	96.365%
35	1000000	0.002	99.827%

ECM Summary

B1	B2	curves	GHz-days
50000	50000	7	0.375
50000	5000000	142	13.02
50000	5200000	7	0.653
50000	6750000	7	0.736
50000	7000000	7	0.750

ECM Details

										GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-02-08T03:59:00	Johan Koolwaaij	C0B5A3B75	50000	5000000						3	0.275
2010-03-12T17:36:00	James Classen	towerofart	50000	5000000						3	0.275
2012-05-11T07:18:00	omiXorp	LLB16-T5500-21	50000	5000000						3	0.275
2014-01-08T22:26:00	Andy Incline	Office-PC	50000	5000000						3	0.275
2015-07-10T02:55:00	guru	w6	50000	5000000						3	0.275
2016-04-25T06:18:23	Jason U	Server7	50000	5000000						3	0.275
2016-06-17T05:40:48	Jason U	Server7	50000	5000000						3	0.275
2016-11-02T23:54:39	Bruce	Desk6	50000	5000000						3	0.275
2017-05-08T06:10:13	Bruce	Desk6	50000	5000000						3	0.275
2017-12-04T01:12:10	Yan Jinzhao	cndns	50000	5000000						3	0.275
2018-05-26T01:45:05	Bruce	Desk6	50000	5000000						3	0.275
2019-07-09T23:35:53	Chang Chia-Tche	ex-ctcpc	50000	5000000						3	0.275
2020-04-29T10:59:58	MarkS	desktop-i7	50000	5000000						3	0.275
2020-05-09T18:51:49	Greg Hogan	azure4	50000	5000000						3	0.275
2020-05-24T02:13:42	mnd9	75203	50000	5000000						3	0.275
2020-06-12T10:40:08	mnd9	25836b	50000	5000000						3	0.275
2020-06-27T06:39:20	GAN	LMS-12	50000	5000000						3	0.275
2020-07-04T11:56:49	GAN	LMS-08	50000	5000000						3	0.275
2020-07-11T03:36:12	GAN	LMS-06	50000	5000000						3	0.275
2020-07-16T22:49:34	GAN	LMS-15	50000	5000000						3	0.275
2020-07-24T01:06:04	Nesowa	entropy_generator_2	50000	5000000						3	0.275
2020-08-06T12:58:55	GAN	PG-HP	50000	5000000						3	0.275
2020-08-14T23:42:37	daveward2005	Dave2	50000	5000000						3	0.275
2020-08-16T01:43:16	M. R. Mayer	nimbus	50000	5000000						3	0.275
2020-09-08T12:37:05	M. R. Mayer	nimbus	50000	5000000						7	0.642
2020-10-09T20:55:37	mnd9	kitchen	50000	5000000						7	0.642
2020-11-09T00:21:39	LaurV	debilis	50000	5000000						7	0.642
2020-12-12T15:44:03	C.D.B.	i7-6850K	50000	5000000						7	0.642
2021-01-07T02:47:50	Cork	Manual testing	50000	5000000						7	0.642
2021-02-12T22:46:22	Zenzoma	AM3700X_1	50000	5000000						7	0.642
2021-03-14T01:13:28	Zenzoma	AMD3970X	50000	5000000						7	0.642
2021-04-22T10:04:37	Rift is Hell	Main	50000	5000000						7	0.642
2021-06-11T11:01:12	kutens	arcturus	50000	5200000						7	0.653
2021-07-23T14:42:22	kutens	terra	50000	6750000						7	0.736
2021-09-25T13:23:29	TyZhou	TyZhou	50000	50000						7	0.375
2021-10-06T15:01:18	Kamil Mudrunka	LinuxServer	50000	5000000						7	0.642
2022-03-11T08:15:37	MarkS	desktop-i7	50000	7000000						7	0.750
2022-05-01T11:58:45	daveward2005	Dave2	50000	5000000						7	0.642

date	userid	compid	res64	spent (GHz-days)
2015-11-15T03:19:13	MadPoo	Manual testing	DD709911231CCB53	0.170

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 = 3730000, B2 = 414030000 (P-1 stage 2)

B1 = 3102822, B2 = 43439508 (P-1 stage 2)

B1 = 3730000 (P-1 stage 1)

B1 = 3102822 (P-1 stage 1)

B1 = 95000, B2 = 1947500 (P-1 stage 2)

B1 = 95000 (P-1 stage 1)

B1 = 15000, B2 = 232500 (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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10⁹

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