M2724047 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	21.8810	67.6471%	600000	6000000	0.1001	4.0831%	21.9811	68.9681%	1.3210%
PrimeNet	2⁵⁹	0.0282	62.7119%	12000	220000	0.0026	2.8476%	0.0308	63.7737%	1.0618%
GPU72	2⁶³	0.5859	65.0794%	14000	240000	0.0029	1.7059%	0.5888	65.6751%	0.5957%
Difference	+5	+21.2951	+2.5677%	+586000	+5760000	+0.0972	+2.3772%	+21.3923	+3.2930%	+3.2930%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2724047	13165117530791749610831	23	73.479	2416462992523945 5 × 483292598504789	2021-01-20	5	483292598504789	1,225.9	2,948,884	5,507,693

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2003-11-16T00:00:00	ANONYMOUS	v4_computers	2048	204800		-		-	-	0.001	-	-	0.241%
2003-11-28T00:00:00	Team Prime Rib	v4_computers	15000	221250		-		-	-	0.003	-	-	0.793%
2010-12-19T21:42:00	Jocelyn Larouche	Manual testing	20000	20000		-		-	-	0.002	-	-	0.269%
2010-12-28T02:15:00	Jocelyn Larouche	Manual testing	30000	30000		-		-	-	0.003	-	-	0.372%
2011-01-18T22:18:00	Jocelyn Larouche	Manual testing	50000	50000		-		-	-	0.006	-	-	0.538%
2011-02-24T13:33:00	James Heinrich	i7-920	300000	8000000		-		-	-	0.081	-	-	3.994%
2018-08-20T10:32:22	Jocelyn Larouche	low 4M	600000	6000000	6	-		-	-	0.100	-	-	4.083%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1998-06-07T00:00:00	BJB	v4_computers	2¹	2⁵⁹		-	-	0.028	-	-
2016-02-23T16:29:20	Mark Rose	Manual testing	2⁵⁹	2⁶⁰		-	-	0.028	-	-
2009-01-28T20:06:00	Sturle Sunde	gimo.ifi	2⁶⁰	2⁶¹		-	-	0.056	-	-
2012-04-18T10:21:00	Grant McCracken	thumper	2⁶¹	2⁶²		-	-	0.113	-	-
2013-01-14T12:26:00	dbaugh	Manual testing	2⁶²	2⁶³		-	-	0.360	-	-
2015-04-13T20:09:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.721	-	-
2015-04-13T20:09:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.372	-	-
2016-01-31T12:58:56	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	2.743	-	-
2017-10-05T11:09:27	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	5.486	-	-
2019-02-12T09:01:42	chuenkit	Manual testing	2⁶⁷	2⁶⁸		-	-	10.97	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	8.034 GHz-days
Estimated T-Level:	3.850

Digits	B1	Curves	Complete	FacMiss
20	11000	77 / 100	0.770	46.122%
25	50000	77 / 280	0.275	75.920%

New Calculation Method

Total ECM effort:	8.034 GHz-days
Estimated T-Level:	3.850

Digits	B1	Complete	FacMiss
20	11000	2.491	8.286%
25	50000	0.225	79.833%
30	250000	0.014	98.622%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		74	7.676
50000	6750000	13165117530791749610831	3	0.358

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-03-13T18:14:00	Smurgs	23-3-06	50000	5000000						3	0.311
2010-08-23T09:34:00	James Classen	towerofart	50000	5000000						3	0.311
2013-02-09T15:30:00	MadPoo	IntLAVH03	50000	5000000						3	0.311
2015-02-22T19:18:00	Jason U	Server7	50000	5000000						3	0.311
2016-02-07T07:32:57	Jason U	Server7	50000	5000000						3	0.311
2016-05-04T20:04:05	lettp	Home	50000	5000000						3	0.311
2017-01-05T21:41:48	deo2016	deo2016.home.new	50000	5000000						3	0.311
2017-07-19T08:16:42	Sebastian Hornbostel	V2	50000	5000000						3	0.311
2017-12-07T19:08:44	Yan Jinzhao	cndns	50000	5000000						3	0.311
2018-08-01T09:34:41	Chang Chia-Tche	ex-ctcpc	50000	5000000						3	0.311
2019-11-04T09:49:03	monsted	rootweiler	50000	5000000						3	0.311
2020-08-02T04:35:01	GAN	LMS-18	50000	5000000						3	0.311
2020-08-09T22:31:18	GAN	LMS-15	50000	5000000						3	0.311
2020-08-22T13:35:41	-Anonymous-	aws	50000	5000000						7	0.726
2020-09-26T05:43:05	daveward2005	Dave2	50000	5000000						7	0.726
2020-11-28T23:35:52	LaurV	debilis	50000	5000000						7	0.726
2020-12-31T12:24:12	Dylan Delgado	colab	50000	5000000						7	0.726
2021-01-07T02:47:56	Cork	Manual testing	50000	5000000						7	0.726
2021-01-20T09:39:37	nordi	sweet16	50000	6750000	13165117530791749610831	73.479	3	2	2265507665740068	3	0.358

date	userid	compid	res64	spent (GHz-days)
1998-07-21T00:00:00	ANONYMOUS	v4_computers	D33CE1688BB4A8F1	0.210
1998-09-27T00:00:00	ANONYMOUS	v4_computers	D33CE1688BB4A8F1	0.210
1999-05-23T00:00:00	ANONYMOUS	v4_computers	D33CE1688BB4A8F1	0.210

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 = 221250 (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

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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