M3048737 Mersenne number exponent details

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M3048737

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>>>

is 2 ^3048737 - 1

has 917762 decimal digits

takes 0.259 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	911BEA9A72565F76	double-checked
PRP	-unknown-	-unknown-

	Trial Factoring			P-1 Factoring				Combined
	Limit	GHz-days	Probability	B1	B2	GHz-days	Probability	GHz-days	Probability	Prob over default TF
Actual	2⁶⁹	39.1594	68.1159%	3048737	667675470	4.8451	9.6656%	44.0045	71.1977%	3.0818%
PrimeNet	2⁶⁰	0.0504	63.3333%	12000	220000	0.0029	2.5226%	0.0533	64.2583%	0.9250%
GPU72	2⁶⁴	1.1675	65.6250%	14000	220000	0.0031	1.4648%	1.1706	66.1285%	0.5035%
Difference	+5	+37.9920	+2.4909%	+3034737	+667455470	+4.8419	+8.2007%	+42.8339	+5.0692%	+5.0692%

Known prime factors (1 factor, 104.7 bits, 0.00343567% 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
3048737	33982079517287838484859567576857	32	104.745	5573140536111812610412044 2² × 3 × 1483 × 1759 × 9049 × 680767 × 28900987	2017-09-18	680767	28900987	6.054e+10	0.2738	0.3629

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2003-12-23T00:00:00	Team Prime Rib	v4_computers	10000	10000		-		-	-	0.001	-	-	0.121%
2004-02-07T00:00:00	ANONYMOUS	v4_computers	2048	204800		-		-	-	0.002	-	-	0.201%
2010-10-03T22:29:00	markr	tiny	110000	2447500		-		-	-	0.029	-	-	2.369%
2016-03-14T11:21:42	Squeeky_Squirrel	P4_2600	205000	5688750	12	-		-	-	0.062	-	-	3.206%
2017-09-18T19:08:10	mikr	MSI	3000000	100000000	12		33982079517287838484859567576857	32	104.745	1.022	0.519	2.045	7.406%
2020-05-15T14:24:10	Jocelyn Larouche	Manual testing	772312	3048737		-		-	-	0.111	-	-	3.239%
2021-11-20T13:50:21	Jocelyn Larouche	Manual testing	3048737	3048737		-		-	-	0.376	-	-	3.377%
2021-12-08T02:49:32	Jocelyn Larouche	Manual testing	3048737	30487370	12	-	skipped known factor: 33982079517287838484859567576857	-	-	0.561	-	-	6.022%
2021-12-21T15:51:57	Jocelyn Larouche	Manual testing	3048737	139246800		-	skipped known factor: 33982079517287838484859567576857	-	-	1.292	-	-	7.806%
2021-12-22T09:19:35	Jocelyn Larouche	Manual testing	3048737	667675470		-	skipped known factor: 33982079517287838484859567576857	-	-	4.845	-	-	9.666%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2001-05-27T00:00:00	ANONYMOUS	v4_computers	2¹	2⁶⁰		-	-	0.050	-	-
2009-02-14T01:35:00	Sturle Sunde	gonsha.ifi	2⁶⁰	2⁶¹		-	-	0.050	-	-
2010-11-13T01:58:00	Sid & Andy	Buzz	2⁶¹	2⁶²		-	-	0.101	-	-
2013-01-07T13:54:00	dbaugh	Manual testing	2⁶²	2⁶³		-	-	0.322	-	-
2015-02-07T18:28:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.644	-	-
2015-02-07T18:28:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.226	-	-
2015-06-06T19:31:00	Tha	Manual testing	2⁶⁵	2⁶⁶		-	-	2.451	-	-
2021-01-16T21:12:25	Jocelyn Larouche	Manual testing	2⁶⁵	2⁶⁶		-	-	2.451	-	-
2021-02-18T11:47:34	Jocelyn Larouche	Manual testing	2⁶⁶	2⁶⁷		-	-	4.902	-	-
2017-05-07T02:13:04	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	4.902	-	-
2021-02-25T22:13:20	Jocelyn Larouche	Manual testing	2⁶⁷	2⁶⁸		-	-	9.80	-	-
2022-01-09T11:52:12	Jocelyn Larouche	Manual testing	2⁶⁸	2⁶⁹		-	-	19.61	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	1.747 GHz-days
Estimated T-Level:	0.750

Digits	B1	Curves	Complete	FacMiss
20	11000	15 / 100	0.150	86.006%
25	50000	15 / 280	0.054	94.775%

New Calculation Method

Total ECM effort:	1.747 GHz-days
Estimated T-Level:	0.750

Digits	B1	Complete	FacMiss
20	11000	0.484	61.639%
25	50000	0.044	95.721%
30	250000	0.003	99.731%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		15	1.747

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-04-17T08:58:00	Helgen	newone	50000	5000000						3	0.349
2011-06-14T06:55:00	sannerud.com	Jim2010	50000	5000000						3	0.349
2013-10-21T07:32:00	Richard Kint	xps	50000	5000000						3	0.349
2016-01-30T11:50:06	Bruce	Desk7	50000	5000000						3	0.349
2017-09-02T00:27:01	storm5510	7700_Kaby_Lake	50000	5000000						3	0.349

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1999-09-14T00:00:00	ANONYMOUS	v4_computers	911BEA9A72565F76	0.259

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-28T09:13:14

Oliver Kruse

GTX-1

33982079517287838484859567576857

A20416CA7CEAF4__

2017-12-10T23:53:01

kkmrkkblmbrbk

c4.xlarge

33982079517287838484859567576857

A20416CA7CEAF4__

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 = 3048737, B2 = 667675470 (P-1 stage 2)

B1 = 3048737, B2 = 139246800 (P-1 stage 2)

B1 = 3000000, B2 = 100000000 (P-1 stage 2)

B1 = 3048737, B2 = 30487370 (P-1 stage 2)

B1 = 3048737 (P-1 stage 1)

B1 = 3000000 (P-1 stage 1)

B1 = 772312, B2 = 3048737 (P-1 stage 2)

B1 = 772312 (P-1 stage 1)

B1 = 205000, B2 = 5688750 (P-1 stage 2)

B1 = 110000, B2 = 2447500 (P-1 stage 2)

B1 = 205000 (P-1 stage 1)

B1 = 110000 (P-1 stage 1)

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

B1 = 10000 (P-1 stage 1)

B1 = 2048 (P-1 stage 1)

10²

10³

10⁴

10⁵

10⁶

10⁷

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

TF factor-bounds graph:

2⁶⁹

2⁶⁸

2⁶⁷

2⁶⁶

2⁶⁵

2⁶⁴

2⁶³

2⁶²

2⁶¹

2⁶⁰

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

2¹¹⁰

Last modified: 2022-01-09T11:52:12+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