M2775043 Mersenne number exponent details

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M2775043

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is 2 ^2775043 - 1

has 835372 decimal digits

takes 0.214 GHz-days to do one PRP test

Last-known PrimeNet details:

Exponent is not assigned to anyone

0 primality tests remaining

	Residue	Status
L-L	7C3BC73B1E0CC369	double-checked
PRP	0E2FE5A0CB32DF0A	verified PRP

	Trial Factoring			P-1 Factoring				Combined
	Limit	GHz-days	Probability	B1	B2	GHz-days	Probability	GHz-days	Probability	Prob over default TF
Actual	2⁶⁸	21.4789	67.6471%	2700000	84000000	0.7984	7.6836%	22.2773	70.1329%	2.4859%
PrimeNet	2⁵⁹	0.0277	62.7119%	12000	220000	0.0026	2.8572%	0.0303	63.7772%	1.0654%
GPU72	2⁶³	0.5751	65.0794%	15000	240000	0.0031	1.7469%	0.5782	65.6894%	0.6100%
Difference	+5	+20.9038	+2.5677%	+2685000	+83760000	+0.7954	+5.9368%	+21.6992	+4.4436%	+4.4436%

Known prime factors (1 factor, 70.1 bits, 0.00252541% known):

Remaining cofactor is not a probable-prime

						P-1		GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2775043	1248894740878624687721	22	70.081	225022592601020 2² × 5 × 11251129630051	2020-10-21	5	11251129630051	144.67	68,650	128,220

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	-	-	0.242%
2010-11-10T22:06:00	Jocelyn Larouche	Manual testing	15000	15000		-		-	-	0.002	-	-	0.210%
2010-11-28T19:57:00	markr	tiny	110000	2392500		-		-	-	0.026	-	-	2.614%
2016-08-27T21:43:39	Jocelyn Larouche	low4M	142000	4785000	6	-		-	-	0.044	-	-	3.195%
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%
2017-03-09T21:09:31	mikr	MSI	2700000	84000000	12	-		-	-	0.798	-	-	7.684%
2017-03-20T01:07:00	Jocelyn Larouche	low 4M	353341	3533410	6	-		-	-	0.059	-	-	3.421%
2017-03-23T15:51:54	Jocelyn Larouche	low 4M	424009	4240090	6	-		-	-	0.071	-	-	3.646%

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	-	-
2009-01-29T02:07:00	Sturle Sunde	bruckner.ifi	2⁶⁰	2⁶¹		-	-	0.055	-	-
2012-03-24T13:22:00	Grant McCracken	thumper	2⁶¹	2⁶²		-	-	0.111	-	-
2013-01-14T12:31:00	dbaugh	Manual testing	2⁶²	2⁶³		-	-	0.354	-	-
2015-04-21T09:20:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.707	-	-
2015-04-21T09:20:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.346	-	-
2015-12-07T04:59:49	omylist	Manual testing	2⁶⁵	2⁶⁶		-	-	2.693	-	-
2017-10-12T12:41:22	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	5.386	-	-
2019-02-24T11:40:38	chuenkit	Manual testing	2⁶⁷	2⁶⁸		-	-	10.77	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	5.202 GHz-days
Estimated T-Level:	2.500

Digits	B1	Curves	Complete	FacMiss
20	11000	50 / 100	0.500	60.501%
25	50000	50 / 280	0.179	83.620%

New Calculation Method

Total ECM effort:	5.202 GHz-days
Estimated T-Level:	2.500

Digits	B1	Complete	FacMiss
20	11000	1.613	19.931%
25	50000	0.146	86.435%
30	250000	0.009	99.106%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		47	4.890
50000	5000000	1248894740878624687721	3	0.312

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-03-19T19:42:00	Lukasz Wrobel	LINUX_01	50000	5000000						3	0.312
2010-09-24T12:50:00	James Hintz	ryan	50000	5000000						3	0.312
2013-03-08T12:41:00	Donna Noble	CCI_PH2_955	50000	5000000						3	0.312
2015-03-16T00:58:00	Jason U	Server7	50000	5000000						3	0.312
2016-02-15T09:24:50	Sintax	cloud	50000	5000000						3	0.312
2016-05-22T11:08:54	Jason U	Server7	50000	5000000						3	0.312
2017-01-25T17:46:36	Bruce	eleven	50000	5000000						3	0.312
2017-08-03T05:41:20	Tom Bammann	Laura-Laptop	50000	5000000						3	0.312
2018-01-08T14:10:59	Conductor	Andrew	50000	5000000						3	0.312
2018-10-20T13:05:19	Chang Chia-Tche	ex-ctcpc	50000	5000000						3	0.312
2020-08-08T22:22:04	IanGlencross	glenx24	50000	5000000						3	0.312
2020-08-18T15:34:06	GAN	OSB-01	50000	5000000						7	0.728
2020-09-21T00:53:24	mnd9	25836b	50000	5000000						7	0.728
2020-10-21T18:01:58	mnd9	75203b	50000	5000000	1248894740878624687721	70.081	3	2	4046707531324967	3	0.312

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1997-12-04T00:00:00	ANONYMOUS	v4_computers	7C3BC73B1E0CC369	0.214
1999-07-04T00:00:00	ANONYMOUS	v4_computers	7C3BC73B1E0CC369	0.214
2018-08-23T20:23:10	kkmrkkblmbrbk	old	7C3BC73B1E0CC369	0.214

PRP results:

date

userid

compid

cofactors

res64

PRP

2020-10-21T19:23:01

mrh

1248894740878624687721

0E2FE5A0CB32DF0A

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 = 424009, B2 = 4240090 (P-1 stage 2)

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

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

B1 = 424009 (P-1 stage 1)

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)

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

10¹²

10¹³

10¹⁴

TF factor-bounds graph:

2⁶⁸

2⁶⁷

2⁶⁶

2⁶⁵

2⁶⁴

2⁶³

2⁶²

2⁶¹

2⁶⁰

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

Last modified: 2020-10-21T19:23:01+00:00

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