M2780501 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	21.4367	67.6471%	2700000	84000000	0.7984	7.6852%	22.2352	70.1334%	2.4864%
PrimeNet	2⁵⁹	0.0276	62.7119%	12000	220000	0.0026	2.8582%	0.0302	63.7776%	1.0658%
GPU72	2⁶³	0.5740	65.0794%	15000	240000	0.0031	1.7475%	0.5771	65.6896%	0.6102%
Difference	+5	+20.8627	+2.5677%	+2685000	+83760000	+0.7954	+5.9376%	+21.6581	+4.4438%	+4.4438%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2780501	29291413883435949582089	23	74.633	5267290657949044 2² × 31² × 311 × 4405990091	2020-11-28	961	4405990091	1,752.4	26.884	50.211

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2003-11-17T00:00:00	ANONYMOUS	v4_computers	2048	204800		-		-	-	0.001	-	-	0.242%
2010-11-10T22:07:00	Jocelyn Larouche	Manual testing	15000	15000		-		-	-	0.002	-	-	0.210%
2010-11-26T18:49:00	markr	tiny	110000	2392500		-		-	-	0.026	-	-	2.615%
2016-08-27T21:43:40	Jocelyn Larouche	low4M	142000	4785000	6	-		-	-	0.044	-	-	3.196%
2016-10-27T01:50:45	Jocelyn Larouche	low 4M	170400	170400		-		-	-	0.019	-	-	1.130%
2016-12-24T02:28:28	Jocelyn Larouche	low 4M	204480	204480		-		-	-	0.023	-	-	1.242%
2017-02-25T21:07:58	Jocelyn Larouche	low 4M	294451	2944510	6	-		-	-	0.049	-	-	3.204%
2017-03-23T15:51:54	Jocelyn Larouche	low 4M	353341	3533410	6	-		-	-	0.059	-	-	3.422%
2017-04-01T13:34:33	mikr	MSI	2700000	84000000	12	-		-	-	0.798	-	-	7.685%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2016-02-23T16:29:21	Mark Rose	Manual testing	2¹	2⁶⁰		-	-	0.055	-	-
2009-01-28T01:48:00	Sturle Sunde	gicy.ifi	2⁶⁰	2⁶¹		-	-	0.055	-	-
2012-03-15T19:45:00	Grant McCracken	home	2⁶¹	2⁶²		-	-	0.110	-	-
2013-01-10T10:21:00	dbaugh	Manual testing	2⁶²	2⁶³		-	-	0.353	-	-
2015-04-21T09:20:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.706	-	-
2015-04-21T09:20:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.344	-	-
2015-12-20T08:25:37	omylist	Manual testing	2⁶⁵	2⁶⁶		-	-	2.688	-	-
2017-10-16T21:21:13	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	5.375	-	-
2019-02-24T11:40:40	chuenkit	Manual testing	2⁶⁷	2⁶⁸		-	-	10.75	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	6.140 GHz-days
Estimated T-Level:	2.950

Digits	B1	Curves	Complete	FacMiss
20	11000	59 / 100	0.590	55.268%
25	50000	59 / 280	0.211	80.970%

New Calculation Method

Total ECM effort:	6.140 GHz-days
Estimated T-Level:	2.950

Digits	B1	Complete	FacMiss
20	11000	1.903	14.909%
25	50000	0.172	84.197%
30	250000	0.011	98.946%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		54	5.620
50000	5000000	29291413883435949582089	5	0.520

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-03-16T17:44:00	Smurgs	Praca	50000	5000000						3	0.312
2010-09-28T14:45:00	James Classen	towerofart	50000	5000000						3	0.312
2013-03-11T16:57:00	Donna Noble	PH2x6	50000	5000000						3	0.312
2015-03-16T23:50:00	Bruce	desk16	50000	5000000						3	0.312
2016-02-15T00:07:25	Sintax	cloud2	50000	5000000						3	0.312
2016-05-24T02:54:29	lettp	Home	50000	5000000						3	0.312
2017-01-30T17:23:16	Bruce	eleven	50000	5000000						3	0.312
2017-08-06T05:22:27	Chang Chia-Tche	ex-ctcpc	50000	5000000						3	0.312
2018-01-10T19:13:15	Sebastian Hornbostel	V2	50000	5000000						3	0.312
2018-11-08T05:15:16	Palantsevich	OfficeB01	50000	5000000						3	0.312
2020-08-10T10:35:42	daveward2005	Dave2	50000	5000000						3	0.312
2020-08-25T02:37:06	Chang Chia-Tche	ex-ctcpc	50000	5000000						7	0.728
2020-10-23T21:37:38	daveward2005	Dave2	50000	5000000						7	0.728
2020-11-27T01:07:14	lycorn	colab_ES	50000	5000000						7	0.728
2020-11-28T06:07:39	daveward2005	Dave2	50000	5000000	29291413883435949582089	74.633	5	2	8265617942796604	5	0.520

date	userid	compid	res64	spent (GHz-days)
1999-06-15T00:00:00	ANONYMOUS	v4_computers	E629CE9E89AD6483	0.215
2018-08-25T10:37:34	kkmrkkblmbrbk	old	E629CE9E89AD6483	0.215

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 = 2700000, B2 = 84000000 (P-1 stage 2)

B1 = 2700000 (P-1 stage 1)

B1 = 353341, B2 = 3533410 (P-1 stage 2)

B1 = 294451, B2 = 2944510 (P-1 stage 2)

B1 = 142000, B2 = 4785000 (P-1 stage 2)

B1 = 353341 (P-1 stage 1)

B1 = 294451 (P-1 stage 1)

B1 = 110000, B2 = 2392500 (P-1 stage 2)

B1 = 204480 (P-1 stage 1)

B1 = 170400 (P-1 stage 1)

B1 = 142000 (P-1 stage 1)

B1 = 110000 (P-1 stage 1)

B1 = 15000 (P-1 stage 1)

B1 = 2048, B2 = 204800 (P-1 stage 2)

B1 = 2048 (P-1 stage 1)

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10¹

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