M710971 Mersenne number exponent details

is 2 ⁷¹⁰⁹⁷¹ - 1

has 214024 decimal digits

takes 0.014 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	41.7934	70.1493%	21000000	900000000	1.9950	11.5922%	43.7885	73.6096%	3.4603%
PrimeNet	2⁴⁰	0.0000	50.0000%	6500	260000	0.0006	21.5099%	0.0006	60.7550%	10.7550%
GPU72	2⁴⁴	0.0000	54.5455%	12000	450000	0.0010	16.5293%	0.0010	62.0588%	7.5133%
Difference	+23	+41.7934	+15.6038%	+20988000	+899550000	+1.9940	-4.9372%	+43.7874	+11.5508%	+11.5508%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
710971	10020504063644516958035515327	29	93.017	7047055409886280142253 3⁵ × 82883 × 349893561094837	2021-05-01	82883	349893561094837	3.794e+9	552,064	1,031,102

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2000-12-07T00:00:00	Alex Kruppa	v4_computers	100000	4000000		-		-	-	0.009	-	-	2.635%
2002-05-25T00:00:00	ANONYMOUS	v4_computers	16384	1638400		-		-	-	0.003	-	-	1.244%
2002-07-06T00:00:00	ANONYMOUS	v4_computers	32768	3276800		-		-	-	0.006	-	-	1.871%
2002-11-02T00:00:00	ANONYMOUS	v4_computers	65537	6553700		-		-	-	0.012	-	-	2.638%
2002-11-16T00:00:00	ANONYMOUS	v4_computers	65537	6553700		-		-	-	0.012	-	-	2.638%
2003-06-09T00:00:00	ANONYMOUS	v4_computers	131072	13107200		-		-	-	0.024	-	-	3.532%
2008-11-17T01:13:00	Jayson King	atlas	5000000	160000000		-		-	-	0.389	-	-	8.422%
2016-05-18T10:31:08	mikr	S058	21000000	900000000	12	-		-	-	1.995	-	-	11.592%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1999-12-08T00:00:00	ANONYMOUS	v4_computers	2⁵³	2⁵⁴		-	-	0.002	-	-
2000-05-10T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁵		-	-	0.007	-	-
2001-04-01T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁶		-	-	0.014	-	-
2001-10-20T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁷		-	-	0.027	-	-
2003-09-21T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.054	-	-
2008-10-12T07:41:00	Sturle Sunde	hummel.ifi	2⁵⁸	2⁵⁹		-	-	0.054	-	-
2008-10-12T08:19:00	Sturle Sunde	hummel.ifi	2⁵⁹	2⁶⁰		-	-	0.108	-	-
2010-06-29T22:20:00	Architects Cubed	m1_fw	2⁶⁰	2⁶¹		-	-	0.216	-	-
2015-02-27T10:54:00	NR	Manual testing	2⁶¹	2⁶²		-	-	0.432	-	-
2015-10-13T09:16:57	Gordon Spence	Manual testing	2⁶²	2⁶³		-	-	1.381	-	-
2015-10-13T09:16:57	Gordon Spence	Manual testing	2⁶³	2⁶⁴		-	-	2.761	-	-
2017-01-19T00:51:03	Conductor	Manual testing	2⁶⁴	2⁶⁵		-	-	5.255	-	-
2017-07-04T03:25:50	Smok_bmv	Manual testing	2⁶⁵	2⁶⁶		-	-	10.51	-	-
2020-05-08T00:19:25	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	21.02	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	12.084 GHz-days
Estimated T-Level:	25.398

Digits	B1	Curves	Complete	FacMiss
20	11000	331 / 100	3.310	3.591%
25	50000	331 / 280	1.182	30.597%
30	250000	51 / 640	0.080	92.335%

New Calculation Method

Total ECM effort:	12.084 GHz-days
Estimated T-Level:	25.398

Digits	B1	Complete	FacMiss
20	11000	13.282	0.000%
25	50000	1.431	23.912%
30	250000	0.117	88.995%
35	1000000	0.008	99.221%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		280	6.324
250000	25000000		44	4.969
250000	25000000	10020504063644516958035515327	7	0.791

ECM Details

										GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2007-08-29T04:40:00	Chad Davis	Bayes	50000	5000000						1	0.023
2007-12-27T11:40:00	Steve Scott	Asus-1	50000	5000000						1	0.023
2007-12-27T16:12:00	Steve Scott	Asus-1	50000	5000000						1	0.023
2008-06-13T07:52:00	Scott Kurowski	UW2	50000	5000000						3	0.068
2008-11-04T20:49:00	Sturle Sunde	v21	50000	5000000						3	0.068
2009-02-01T20:44:00	Sturle Sunde	v23	50000	5000000						3	0.068
2009-07-06T19:28:00	Architects Cubed	m1_52	50000	5000000						3	0.068
2009-07-25T19:07:00	Sturle Sunde	v26	50000	5000000						3	0.068
2009-07-29T18:59:00	Sturle Sunde	PREUSW40604NL	50000	5000000						3	0.068
2009-09-11T01:51:00	Sturle Sunde	FKWXPTESTEIK	50000	5000000						3	0.068
2009-10-15T02:49:00	Sturle Sunde	TOR-ST-0024	50000	5000000						3	0.068
2009-11-06T09:45:00	linded	KCPB8P0-NET214	50000	5000000						3	0.068
2009-11-30T00:59:00	Sturle Sunde	FKWXPTESTEIK	50000	5000000						3	0.068
2009-12-28T17:10:00	Sturle Sunde	TOR-ST-0024	50000	5000000						3	0.068
2010-01-20T12:23:00	James Hintz	03_122109	50000	5000000						3	0.068
2010-02-06T20:33:00	Sturle Sunde	TOR-ST-0020	50000	5000000						3	0.068
2010-03-02T04:34:00	Sturle Sunde	FKWXPTESTEIK	50000	5000000						3	0.068
2010-03-25T05:58:00	Sturle Sunde	FKWXPTESTEIK	50000	5000000						3	0.068
2010-04-15T08:46:00	Sturle Sunde	FKWXPTESTEIK	50000	5000000						3	0.068
2010-05-06T21:04:00	Sturle Sunde	FKWXPTESTEIK	50000	5000000						3	0.068
2010-05-29T15:06:00	Sturle Sunde	FKWXPTESTEIK	50000	5000000						3	0.068
2010-06-30T15:50:00	Sturle Sunde	FKWXPTESTEIK	50000	5000000						3	0.068
2010-07-30T20:51:00	Sturle Sunde	FKWXPTESTEIK	50000	5000000						3	0.068
2010-08-28T22:11:00	Sturle Sunde	FKWXPTESTEIK	50000	5000000						3	0.068
2010-09-18T23:07:00	Sturle Sunde	FKWXPTESTEIK	50000	5000000						3	0.068
2010-10-09T23:01:00	Sturle Sunde	FKWXPTESTEIK	50000	5000000						3	0.068
2010-10-27T05:35:00	Sturle Sunde	FKWXPTESTEIK	50000	5000000						3	0.068
2010-11-14T19:23:00	Sturle Sunde	FKWXPTESTEIK	50000	5000000						3	0.068
2010-12-05T21:19:00	Sturle Sunde	FKWXPTESTEIK	50000	5000000						3	0.068
2010-12-23T22:43:00	Sturle Sunde	PRECZC5060K5N	50000	5000000						3	0.068
2011-01-13T13:22:00	Damian Silvestre	PcMa	50000	5000000						3	0.068
2011-01-29T05:56:00	Sturle Sunde	FKWXPTESTEIK	50000	5000000						3	0.068
2011-02-18T03:25:00	Sturle Sunde	FKWXPTESTEIK	50000	5000000						3	0.068
2011-03-06T14:04:00	James Hintz	06_122109	50000	5000000						3	0.068
2011-03-20T19:30:00	Sturle Sunde	FKWXPTESTEIK	50000	5000000						3	0.068
2011-04-15T19:41:00	James Hintz	06_122109	50000	5000000						3	0.068
2011-05-08T20:34:00	Lukasz Wrobel	w-l	50000	5000000						3	0.068
2011-05-27T22:46:00	Sturle Sunde	TOR-ST-0038	50000	5000000						3	0.068
2011-06-19T05:47:00	Sturle Sunde	FKWXPTESTEIK	50000	5000000						3	0.068
2011-07-20T17:41:00	Lukasz Wrobel	w-l	50000	5000000						3	0.068
2011-08-24T21:24:00	Sturle Sunde	FKWXPTESTEIK	50000	5000000						3	0.068
2011-11-11T17:23:00	Sturle Sunde	PRECZC5060K5N	50000	5000000						3	0.068
2012-01-15T03:12:00	Sturle Sunde	PRECZC5060K5N	50000	5000000						3	0.068
2012-03-09T06:27:00	Sturle Sunde	TOR-ST-0036	50000	5000000						3	0.068
2012-05-31T20:05:00	Sturle Sunde	TOR-ST-0033	50000	5000000						3	0.068
2012-08-30T16:32:00	Sturle Sunde	TOR-ST-0033	50000	5000000						3	0.068
2013-03-17T02:42:00	Sturle Sunde	PRE6S33KN9ZE3KY	50000	5000000						3	0.068
2013-11-28T12:42:00	Bruce	bfc-ws	50000	5000000						3	0.068
2014-03-29T11:49:00	Bruce	snowflake	50000	5000000						3	0.068
2014-04-01T06:14:00	Bruce	snowflake	50000	5000000						3	0.068
2015-05-12T21:19:00	Nacnud	Calculator	50000	5000000						3	0.068
2015-10-29T08:47:15	Nacnud	Calculator	50000	5000000						3	0.068
2016-01-26T14:43:01	LocTite	Orion	50000	5000000						3	0.068
2016-05-13T16:20:32	TJAOI	Manual testing	50000	5000000						37	0.836
2016-09-18T06:31:19	westicles	Manual testing	50000	5000000						90	2.033
2017-05-09T03:04:37	driveByUpgrades	AMD8	250000	25000000						3	0.339
2018-01-02T21:06:09	Bruce	Desk9	250000	25000000						3	0.339
2018-11-30T11:51:09	TJAOI	Manual testing	250000	25000000						38	4.291
2021-05-01T20:44:55	GAN	N-27	250000	25000000	10020504063644516958035515327	93.017	7	2	7712092419603382	7	0.791

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
2015-04-11T15:45:00	MadPoo	Manual testing	402978341E0F2907	0.014

PRP results:

date

userid

compid

cofactors

res64

PRP

2021-05-02T19:07:54

Yuji HASEGAWA

vj20a

10020504063644516958035515327

3228A19C12F390__

2021-05-03T14:16:34

marssystems

system11

10020504063644516958035515327

3228A19C12F39077

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 = 21000000, B2 = 900000000 (P-1 stage 2)

B1 = 21000000 (P-1 stage 1)

B1 = 5000000, B2 = 160000000 (P-1 stage 2)

B1 = 5000000 (P-1 stage 1)

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

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

B1 = 100000, B2 = 4000000 (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 = 100000 (P-1 stage 1)

B1 = 65537 (P-1 stage 1)

B1 = 32768 (P-1 stage 1)

B1 = 16384 (P-1 stage 1)

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

10¹²

10¹³

10¹⁴

10¹⁵

TF factor-bounds graph:

2⁶⁷

2⁶⁶

2⁶⁵

2⁶⁴

2⁶³

2⁶²

2⁶¹

2⁶⁰

2⁵⁹

2⁵⁸

2⁵⁷

2⁵⁶

2⁵⁵

2⁵⁴

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

Last modified: 2021-05-03T14:16:34+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