M400069 Mersenne number exponent details

is 2 ⁴⁰⁰⁰⁶⁹ - 1

has 120433 decimal digits

takes 0.004 GHz-days to do one PRP test

Exponent is not assigned to anyone

	Trial Factoring	P-1 Factoring	Combined
Limit	GHz-days	Probability	B1	B2	GHz-days	Probability	GHz-days	Probability	Prob over default TF
Actual	2⁶⁷	74.2720	71.6418%	10000000	1000000000	0.8988	10.7667%	75.1708	74.6950%	22.1950%
PrimeNet	2⁴⁰	0.0000	52.5000%	4000	130000	0.0002	17.5231%	0.0002	60.8235%	8.3235%
GPU72	2⁴⁴	0.0000	56.8182%	7000	220000	0.0003	13.0638%	0.0003	62.4594%	5.6412%
Difference	+23	+74.2720	+14.8236%	+9993000	+999780000	+0.8985	-2.2970%	+75.1705	+12.2357%	+12.2357%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
400069	17384946805580300647271050027369	32	103.778	21727435524347425878124836 2² × 3 × 251 × 7213624012067538472153	2013-07-18	251	7213624012067538472153	4.180e+11	5.525e+12	1.032e+13

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2001-11-14T00:00:00	ANONYMOUS	v4_computers	50000	1000000		-		-	-	0.001	-	-	1.452%
2002-06-15T00:00:00	ANONYMOUS	v4_computers	32768	3276800		-		-	-	0.003	-	-	1.689%
2002-08-17T00:00:00	ANONYMOUS	v4_computers	65536	6553600		-		-	-	0.006	-	-	2.408%
2003-03-16T00:00:00	ANONYMOUS	v4_computers	131072	13107200		-		-	-	0.012	-	-	3.255%
2016-03-16T19:24:36	alpertron	Manual testing	3000000	100000000	12	-		-	-	0.116	-	-	7.115%
2016-03-17T15:43:18	alpertron	Manual testing	10000000	1000000000	12	-		-	-	0.899	-	-	10.767%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2001-03-17T00:00:00	ANONYMOUS	v4_computers	?	2⁵⁶		-	-	0.024	-	-
2002-01-02T00:00:00	ANONYMOUS	v4_computers	?	2⁵⁷		-	-	0.048	-	-
2003-11-16T00:00:00	ANONYMOUS	v4_computers	?	2⁵⁸		-	-	0.096	-	-
2008-11-23T17:02:00	monst	mersenne	2⁵⁹	2⁶⁰		-	-	0.192	-	-
2011-09-22T00:00:00	Richard B. Woods	v4_computers	2⁶⁰	2⁶¹		-	-	0.384	-	-
2011-02-08T07:29:00	monst	yuengling	2⁶⁰	2⁶¹		-	-	0.384	-	-
2012-11-11T08:23:00	dbaugh	Manual testing	2⁶¹	2⁶²		-	-	0.768	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	27.703 GHz-days
Estimated T-Level:	28.906

Digits	B1	Curves	Complete	FacMiss
20	11000	630 / 100	6.300	0.178%
25	50000	630 / 280	2.250	10.498%
30	250000	500 / 640	0.781	45.755%

New Calculation Method

Total ECM effort:	27.703 GHz-days
Estimated T-Level:	28.906

Digits	B1	Complete	FacMiss
20	11000	45.860	0.000%
25	50000	6.403	0.166%
30	250000	0.674	50.990%
35	1000000	0.055	94.633%
40	3000000	0.004	99.634%

ECM Summary

B1	B2	factor	curves	GHz-days
		17384946805580300647271050027369	1	0.00000e+0
50000	5000000		130	1.369
250000	25000000		500	26.33

ECM Details

										GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2007-08-14T08:28:00	ANONYMOUS	Bayes	50000	5000000						1	0.011
2007-08-31T10:34:00	Team_Bundu	bundu1	50000	5000000						1	0.011
2007-10-05T11:30:00	Chad Davis	Bayes	50000	5000000						1	0.011
2008-01-07T19:53:00	Team_Bundu	bundu1	50000	5000000						1	0.011
2008-01-08T21:25:00	Team_Bundu	bundu1	50000	5000000						3	0.032
2008-04-20T04:38:00	Sturle Sunde	v17	50000	5000000						3	0.032
2008-09-18T17:14:00	Sturle Sunde	v21	50000	5000000						3	0.032
2008-11-07T04:38:00	Sturle Sunde	v22	50000	5000000						3	0.032
2008-12-15T00:56:00	Sturle Sunde	v23	50000	5000000						3	0.032
2009-02-12T00:49:00	Sturle Sunde	v17	50000	5000000						3	0.032
2009-03-12T01:20:00	Sturle Sunde	v23	50000	5000000						3	0.032
2009-04-11T11:59:00	Lupo	yorick	50000	5000000						3	0.032
2009-06-12T20:41:00	linded	KCPB8P0-NET214	50000	5000000						3	0.032
2009-07-07T15:42:00	For Research	m1_54	50000	5000000						3	0.032
2009-07-10T21:47:00	For Research	m1_58	50000	5000000						3	0.032
2009-08-03T01:35:00	Sturle Sunde	FLB-ST-0034	50000	5000000						3	0.032
2009-09-06T09:25:00	JimBa	CIT3srvr	50000	5000000						3	0.032
2009-09-24T02:50:00	Sturle Sunde	FKWXPTESTEIK	50000	5000000						3	0.032
2009-10-13T16:36:00	Sturle Sunde	FKWXPTESTEIK	50000	5000000						3	0.032
2009-10-25T01:17:00	Sturle Sunde	FKWXPTESTEIK	50000	5000000						3	0.032
2009-11-06T09:52:00	David Bessell	L301	50000	5000000						3	0.032
2009-11-18T03:36:00	Sturle Sunde	FKWXPTESTEIK	50000	5000000						3	0.032
2009-12-02T20:39:00	Sturle Sunde	TOR-ST-0020	50000	5000000						3	0.032
2009-12-16T05:58:00	Sturle Sunde	PREUSW40604NL	50000	5000000						3	0.032
2010-01-01T16:23:00	Sturle Sunde	TOR-ST-0024	50000	5000000						3	0.032
2010-01-14T06:02:00	Sturle Sunde	PRE6S2CKN9ZD4EE	50000	5000000						3	0.032
2010-01-24T02:07:00	Sturle Sunde	FKWXPTESTEIK	50000	5000000						3	0.032
2010-02-02T23:07:00	Sturle Sunde	FKWXPTESTEIK	50000	5000000						3	0.032
2010-02-11T18:02:00	James Hintz	17_012210	50000	5000000						3	0.032
2010-02-27T03:38:00	Sturle Sunde	FKWXPTESTEIK	50000	5000000						3	0.032
2010-03-12T18:56:00	Sturle Sunde	FKWXPTESTEIK	50000	5000000						3	0.032
2010-03-24T20:06:00	Sturle Sunde	FKWXPTESTEIK	50000	5000000						3	0.032
2010-04-04T12:02:00	David Bessell	L301	50000	5000000						3	0.032
2010-04-15T22:14:00	Sturle Sunde	FKWXPTESTEIK	50000	5000000						3	0.032
2010-05-09T03:41:00	Sturle Sunde	FKWXPTESTEIK	50000	5000000						3	0.032
2010-05-21T19:22:00	Sturle Sunde	TOR-ST-0024	50000	5000000						3	0.032
2010-06-03T17:54:00	Sturle Sunde	FKWXPTESTEIK	50000	5000000						3	0.032
2010-06-17T17:27:00	Sturle Sunde	FKWXPTESTEIK	50000	5000000						3	0.032
2010-07-04T02:09:00	Sturle Sunde	FKWXPTESTEIK	50000	5000000						3	0.032
2010-07-11T21:29:00	Sturle Sunde	FKWXPTESTEIK	50000	5000000						3	0.032
2010-07-23T22:28:00	Sturle Sunde	FKWXPTESTEIK	50000	5000000						3	0.032
2010-08-10T03:45:00	Sturle Sunde	FKWXPTESTEIK	50000	5000000						3	0.032
2010-08-26T00:49:00	Sturle Sunde	FKWXPTESTEIK	50000	5000000						3	0.032
2010-09-07T03:07:00	sannerud.com	Jim2010	50000	5000000						3	0.032
2010-09-18T16:32:00	Sturle Sunde	PREUSW40604NL	50000	5000000						3	0.032
2010-09-29T04:31:00	Sturle Sunde	FKWXPTESTEIK	50000	5000000						3	0.032
2010-10-07T11:36:00	alpertron	Manual testing	250000	25000000						100	5.267
2011-03-25T13:53:00	alpertron	Manual testing	250000	25000000						100	5.267
2011-07-28T12:36:00	alpertron	Manual testing	250000	25000000						100	5.267
2011-11-28T19:25:00	alpertron	Manual testing	250000	25000000						200	10.53
2013-07-18T18:50:00	Youcef L	breitner			17384946805580300647271050027369	103.778		1		1	-

Lucas-Lehmer results:
Exponent "400069" not found

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-23T08:57:53

Oliver Kruse

Ollaptop

17384946805580300647271050027369

6469452311599D__

2017-11-02T10:30:24

kkmrkkblmbrbk

c4.xlarge

17384946805580300647271050027369

6469452311599D__

2020-04-18T16:20:17

Oliver Kruse

AddPrpType5

17384946805580300647271050027369

F4B99626EAC3FC__

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 = 10000000, B2 = 1000000000 (P-1 stage 2)

B1 = 10000000 (P-1 stage 1)

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

B1 = 3000000 (P-1 stage 1)

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

B1 = 65536, B2 = 6553600 (P-1 stage 2)

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

B1 = 131072 (P-1 stage 1)

B1 = 50000, B2 = 1000000 (P-1 stage 2)

B1 = 65536 (P-1 stage 1)

B1 = 50000 (P-1 stage 1)

B1 = 32768 (P-1 stage 1)

10¹

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10⁶

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10²

10³

10⁴

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10⁷

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10¹¹

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10¹³

10¹⁴

10¹⁵

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10¹⁸

10¹⁹

10²⁰

10²¹

10²²

TF factor-bounds graph:

2⁶⁷

2⁶²

2⁶¹

2⁶⁰

2⁵⁸

2⁵⁷

2⁵⁶

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

2¹¹⁰

Last modified: 2020-04-18T16:20:17+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