M793841 Mersenne number exponent details

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M793841

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is 2 ⁷⁹³⁸⁴¹ - 1

has 238970 decimal digits

takes 0.016 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	333376A9B55F79F2	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	2⁶⁷	37.4306	70.1493%	500000	15000000	0.0374	4.5794%	37.4679	71.5163%	1.3670%
PrimeNet	2⁴⁰	0.0000	50.0000%	7000	300000	0.0007	22.2938%	0.0007	61.1469%	11.1469%
GPU72	2⁴⁴	0.0000	54.5455%	13000	500000	0.0011	17.1038%	0.0011	62.3199%	7.7744%
Difference	+23	+37.4306	+15.6038%	+487000	+14500000	+0.0362	-12.5243%	+37.4668	+9.1964%	+9.1964%

Known prime factors (2 factors, 152.3 bits, 0.01918017% 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
793841	332314762886589515999	21	68.171	209308137830239 7 × 22441 × 1332434497	2009-07-12	22441	1332434497	86.152	2.1029	3.9266
793841	20572437510779403254518769	26	84.089	12957530230096079224 2³ × 19 × 157 × 542973945277241	2020-03-23	157	542973945277241	6,477,888	856,707	1,600,091

1 Composite Factors:

exponent	prime factors	composite factor	digits	bits*
793841	332314762886589515999 20572437510779403254518769	6836524693393837242629013621449818817371285231	46	152.260

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2002-01-02T00:00:00	ANONYMOUS	v4_computers	2000	200000		-		-	-	0.000	-	-	0.203%
2002-02-10T00:00:00	ANONYMOUS	v4_computers	4096	409600		-		-	-	0.001	-	-	0.434%
2002-03-31T00:00:00	ANONYMOUS	v4_computers	8192	819200		-		-	-	0.002	-	-	0.782%
2002-05-25T00:00:00	ANONYMOUS	v4_computers	16384	1638400		-		-	-	0.003	-	-	1.271%
2002-07-27T00:00:00	ANONYMOUS	v4_computers	32768	3276800		-		-	-	0.006	-	-	1.907%
2002-12-31T00:00:00	ANONYMOUS	v4_computers	65537	6553700		-		-	-	0.012	-	-	2.683%
2003-07-21T00:00:00	ANONYMOUS	v4_computers	131072	13107200		-		-	-	0.024	-	-	3.587%
unknown			500000	15000000		-		-	-	0.037	-	-	4.579%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2000-10-07T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁵		-	-	0.006	-	-
2001-02-11T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁶		-	-	0.012	-	-
2001-12-08T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁷		-	-	0.024	-	-
2003-09-14T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.048	-	-
2008-10-11T05:42:00	Sturle Sunde	iago.ifi	2⁵⁸	2⁵⁹		-	-	0.048	-	-
2008-10-11T06:14:00	Sturle Sunde	iago.ifi	2⁵⁹	2⁶⁰		-	-	0.097	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	11.390 GHz-days
Estimated T-Level:	25.344

Digits	B1	Curves	Complete	FacMiss
20	11000	323 / 100	3.230	3.892%
25	50000	323 / 280	1.154	31.486%
30	250000	44 / 640	0.069	93.351%

New Calculation Method

Total ECM effort:	11.390 GHz-days
Estimated T-Level:	25.344

Digits	B1	Complete	FacMiss
20	11000	14.731	0.000%
25	50000	1.613	19.937%
30	250000	0.131	87.717%
35	1000000	0.009	99.131%

ECM Summary

B1	B2	factor	curves	GHz-days
		332314762886589515999	1	0.00000e+0
50000	5000000		279	6.368
250000	25000000		35	3.994
250000	25000000	20572437510779403254518769	9	1.027

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2007-09-01T21:22:00	Team_Bundu	bundu1	50000	5000000						1	0.023
2008-01-19T00:38:00	Steve Scott	805D	50000	5000000						3	0.068
2008-09-24T13:19:00	Sturle Sunde	v1	50000	5000000						3	0.068
2009-01-07T06:24:00	Sturle Sunde	v24	50000	5000000						3	0.068
2009-03-22T00:09:00	Sturle Sunde	v21	50000	5000000						3	0.068
2009-07-12T07:42:00	SubPrime	c2d0			332314762886589515999	68.171		1		1	-
2015-11-27T11:30:14	TJAOI	Manual testing	50000	5000000						85	1.940
2016-09-09T13:49:50	TJAOI	Manual testing	50000	5000000						90	2.054
2017-08-25T10:17:38	TJAOI	Manual testing	50000	5000000						91	2.077
2020-03-23T10:25:29	TJAOI	Manual testing	250000	25000000	20572437510779403254518769	84.089	9	2		9	1.027
2020-03-23T10:25:29	TJAOI	Manual testing	250000	25000000						35	3.994

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
2002-11-02T00:00:00	ANONYMOUS	v4_computers	333376A9B55F79F2	0.016

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-28T00:53:19

Oliver Kruse

GTX-2

332314762886589515999

EC312030773D62__

2017-10-13T22:15:05

Oliver Kruse

Threadripper

EC312030773D62__

2017-12-17T08:35:13

ATH

ec2-1xf

332314762886589515999

EC312030773D62__

2020-03-23T11:40:06

CrypticClue

cruncher

332314762886589515999

20572437510779403254518769

C60C2F5B3AFE221A

2020-03-26T05:40:28

oodaira

com2

332314762886589515999

20572437510779403254518769

C60C2F5B3AFE221A

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 = 500000, B2 = 15000000 (P-1 stage 2)

B1 = 131072, B2 = 13107200 (P-1 stage 2)

B1 = 500000 (P-1 stage 1)

B1 = 65537, B2 = 6553700 (P-1 stage 2)

B1 = 32768, B2 = 3276800 (P-1 stage 2)

B1 = 131072 (P-1 stage 1)

B1 = 16384, B2 = 1638400 (P-1 stage 2)

B1 = 65537 (P-1 stage 1)

B1 = 8192, B2 = 819200 (P-1 stage 2)

B1 = 32768 (P-1 stage 1)

B1 = 4096, B2 = 409600 (P-1 stage 2)

B1 = 16384 (P-1 stage 1)

B1 = 2000, B2 = 200000 (P-1 stage 2)

B1 = 8192 (P-1 stage 1)

B1 = 4096 (P-1 stage 1)

B1 = 2000 (P-1 stage 1)

10¹

10²

10³

10⁴

10⁵

10⁶

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

10¹²

10¹³

10¹⁴

10¹⁵

TF factor-bounds graph:

2⁶⁷

2⁶⁰

2⁵⁹

2⁵⁸

2⁵⁷

2⁵⁶

2⁵⁵

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

Last modified: 2020-03-26T05:40:28+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