M693421 Mersenne number exponent details

is 2 ⁶⁹³⁴²¹ - 1

has 208741 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	42.8512	70.1493%	10000000	200000000	0.5894	9.0567%	43.4406	72.8527%	2.7035%
PrimeNet	2⁴⁰	0.0000	50.0000%	6500	260000	0.0006	21.4515%	0.0006	60.7258%	10.7258%
GPU72	2⁴⁴	0.0000	54.5455%	12000	450000	0.0010	16.4822%	0.0010	62.0374%	7.4919%
Difference	+23	+42.8512	+15.6038%	+9988000	+199550000	+0.5883	-7.4256%	+43.4395	+10.8154%	+10.8154%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
693421	53038315068198497675402041	26	85.455	38243949251752180620 2² × 3² × 5 × 2621 × 72797 × 1113550007	2021-04-17	72797	1113550007	22,013,207	1.7590	3.2815

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	-	-	0.195%
2002-01-28T00:00:00	ANONYMOUS	v4_computers	4096	409600		-		-	-	0.001	-	-	0.419%
2002-03-16T00:00:00	ANONYMOUS	v4_computers	8192	819200		-		-	-	0.002	-	-	0.759%
2002-05-05T00:00:00	ANONYMOUS	v4_computers	16384	1638400		-		-	-	0.003	-	-	1.238%
2002-07-14T00:00:00	ANONYMOUS	v4_computers	32768	3276800		-		-	-	0.006	-	-	1.862%
2002-10-26T00:00:00	ANONYMOUS	v4_computers	65536	6553600		-		-	-	0.012	-	-	2.627%
2003-06-30T00:00:00	ANONYMOUS	v4_computers	131072	13107200		-		-	-	0.024	-	-	3.520%
2011-07-19T21:09:00	Jocelyn Larouche	Manual testing	320438	320438		-		-	-	0.009	-	-	1.403%
2012-02-17T11:12:00	Jocelyn Larouche	Manual testing	534063	534063		-		-	-	0.015	-	-	1.774%
2012-06-07T12:02:00	alpertron	Manual testing	10000000	200000000		-		-	-	0.589	-	-	9.057%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2000-02-16T00:00:00	ANONYMOUS	v4_computers	2⁵³	2⁵⁴		-	-	0.002	-	-
2022-03-07T09:21:23	LordJulius	Manual testing	2⁵⁴	2⁵⁵		-	-	0.003	-	-
2001-04-08T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁶		-	-	0.014	-	-
2001-12-22T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁷		-	-	0.028	-	-
2003-10-08T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.055	-	-
2008-10-12T08:56:00	Sturle Sunde	hindemith.ifi	2⁵⁸	2⁵⁹		-	-	0.055	-	-
2008-10-12T09:34:00	Sturle Sunde	hindemith.ifi	2⁵⁹	2⁶⁰		-	-	0.111	-	-
2010-11-20T10:16:00	Sid & Andy	Buzz	2⁶⁰	2⁶¹		-	-	0.221	-	-
2015-04-16T09:23:00	lycorn	Manual testing	2⁶¹	2⁶²		-	-	0.443	-	-
2015-11-03T14:18:43	Gordon Spence	Manual testing	2⁶²	2⁶³		-	-	1.416	-	-
2015-11-03T14:18:43	Gordon Spence	Manual testing	2⁶³	2⁶⁴		-	-	2.831	-	-
2017-01-23T15:04:42	Conductor	Manual testing	2⁶⁴	2⁶⁵		-	-	5.388	-	-
2017-08-18T09:30:43	Smok_bmv	Manual testing	2⁶⁵	2⁶⁶		-	-	10.78	-	-
2020-01-09T22:02:08	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	21.55	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	12.701 GHz-days
Estimated T-Level:	25.375

Digits	B1	Curves	Complete	FacMiss
20	11000	335 / 100	3.350	3.450%
25	50000	335 / 280	1.196	30.163%
30	250000	48 / 640	0.075	92.769%

New Calculation Method

Total ECM effort:	12.701 GHz-days
Estimated T-Level:	25.375

Digits	B1	Complete	FacMiss
20	11000	13.296	0.000%
25	50000	1.424	24.069%
30	250000	0.115	89.128%
35	1000000	0.008	99.237%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		287	6.468
250000	25000000		38	4.282
250000	25000000	53038315068198497675402041	5	0.563
250000	128992510		5	1.388

ECM Details

										GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2007-08-28T09:14:00	Chad Davis	Bayes	50000	5000000						1	0.023
2007-12-19T00:53:00	Steve Scott	Abit	50000	5000000						1	0.023
2007-12-19T03:36:00	Steve Scott	Abit	50000	5000000						1	0.023
2008-04-29T03:18:00	arnaud	chamot24	50000	5000000						3	0.068
2008-10-29T16:13:00	Sturle Sunde	v21	50000	5000000						3	0.068
2009-01-23T17:03:00	Sturle Sunde	v21	50000	5000000						3	0.068
2009-03-24T16:09:00	Sturle Sunde	v21	50000	5000000						3	0.068
2009-07-01T15:55:00	Architects Cubed	m1_74	50000	5000000						3	0.068
2009-07-12T02:11:00	Architects Cubed	m1_71	50000	5000000						3	0.068
2009-09-03T22:56:00	Sturle Sunde	FKWXPTESTEIK	50000	5000000						3	0.068
2009-10-06T05:50:00	Sturle Sunde	FKWXPTESTEIK	50000	5000000						3	0.068
2009-10-30T03:08:00	Sturle Sunde	FKWXPTESTEIK	50000	5000000						3	0.068
2009-11-22T11:49:00	linded	KCPB8P0-NET214	50000	5000000						3	0.068
2009-12-17T18:50:00	Sturle Sunde	FKWXPTESTEIK	50000	5000000						3	0.068
2010-01-12T18:47:00	Sturle Sunde	PREUSW40604NL	50000	5000000						3	0.068
2010-01-31T10:55:00	James Hintz	18_012210	50000	5000000						3	0.068
2010-02-19T04:39:00	Sturle Sunde	FKWXPTESTEIK	50000	5000000						3	0.068
2010-03-16T16:19:00	Sturle Sunde	FKWXPTESTEIK	50000	5000000						3	0.068
2010-04-08T07:13:00	James Hintz	05_122109	50000	5000000						3	0.068
2010-04-26T17:04:00	Sturle Sunde	TOR-ST-0025	50000	5000000						3	0.068
2010-05-18T21:02:00	James Hintz	18_051310	50000	5000000						3	0.068
2010-07-12T18:54:00	Sturle Sunde	FKWXPTESTEIK	50000	5000000						3	0.068
2010-08-13T04:07:00	Sturle Sunde	TOR-ST-0024	50000	5000000						3	0.068
2010-08-16T05:30:00	David J. Stucki	ds-cbt	50000	5000000						3	0.068
2010-09-06T23:15:00	Sturle Sunde	0020ED7F6D0F	50000	5000000						3	0.068
2010-09-26T18:44:00	Sturle Sunde	FKWXPTESTEIK	50000	5000000						3	0.068
2010-10-16T03:36:00	Sturle Sunde	TOR-ST-0024	50000	5000000						3	0.068
2010-11-11T18:05:00	Sturle Sunde	TOR-ST-0025	50000	5000000						3	0.068
2010-11-24T17:34:00	Sturle Sunde	FKWXPTESTEIK	50000	5000000						3	0.068
2010-12-10T19:35:00	Beat Bucheli	I7	50000	5000000						3	0.068
2010-12-29T05:33:00	Beat Bucheli	I7	50000	5000000						3	0.068
2011-01-19T07:55:00	James Hintz	06_122109	50000	5000000						3	0.068
2011-02-01T21:31:00	Sturle Sunde	PRECZC5060K5N	50000	5000000						3	0.068
2011-02-20T16:39:00	Sturle Sunde	FKWXPTESTEIK	50000	5000000						3	0.068
2011-03-06T23:24:00	Sturle Sunde	FKWXPTESTEIK	50000	5000000						3	0.068
2011-03-24T08:55:00	James Hintz	06_122109	50000	5000000						3	0.068
2011-04-15T04:22:00	Lukasz Wrobel	w-l	50000	5000000						3	0.068
2011-05-09T21:04:00	Sturle Sunde	FKWXPTESTEIK	50000	5000000						3	0.068
2011-05-28T19:12:00	Sturle Sunde	FKWXPTESTEIK	50000	5000000						3	0.068
2011-06-19T16:19:00	Sturle Sunde	FKWXPTESTEIK	50000	5000000						3	0.068
2011-07-19T22:03:00	Sturle Sunde	FKWXPTESTEIK	50000	5000000						3	0.068
2011-08-23T04:54:00	Lukasz Wrobel	w-l	50000	5000000						3	0.068
2011-10-31T20:09:00	Sturle Sunde	FKWXPTESTEIK	50000	5000000						3	0.068
2012-01-11T05:40:00	Sturle Sunde	FKWXPTESTEIK	50000	5000000						3	0.068
2012-03-02T17:34:00	Sturle Sunde	FKWXPTESTEIK	50000	5000000						3	0.068
2012-05-21T16:46:00	Sturle Sunde	TOR-ST-0033	50000	5000000						3	0.068
2012-08-19T05:50:00	Sturle Sunde	PREUSW40604NL	50000	5000000						3	0.068
2013-02-04T16:47:00	Lackó	Iroda_Laci_uj	50000	5000000						3	0.068
2013-10-01T15:14:00	lopper	Surface_staples	50000	5000000						3	0.068
2014-03-28T09:21:00	Bruce	snowflake	50000	5000000						3	0.068
2014-03-31T08:59:00	Bruce	snowflake	50000	5000000						3	0.068
2014-12-31T13:33:00	Simon Harrison	m002	50000	5000000						3	0.068
2015-09-23T22:43:41	Nacnud	Calculator	50000	5000000						3	0.068
2016-01-22T17:21:36	PeterCrea	prd	50000	5000000						3	0.068
2016-02-25T06:35:15	ANONYMOUS	C272CE75B	50000	5000000						3	0.068
2016-04-28T22:04:47	ANONYMOUS	C272CE75B	50000	5000000						3	0.068
2016-05-22T22:23:53	Bruce J. Wilder	VIPER	50000	5000000						3	0.068
2016-05-31T17:07:04	raman22feb1988	Manual testing	250000	128992510						5	1.388
2016-06-10T14:43:54	TJAOI	Manual testing	50000	5000000						31	0.699
2016-06-11T09:28:48	Bruce J. Wilder	VIPER	50000	5000000						3	0.068
2016-09-25T03:32:04	westicles	Manual testing	50000	5000000						43	0.969
2016-09-27T06:32:16	westicles	Manual testing	50000	5000000						1	0.023
2017-02-10T18:28:42	TJAOI	Manual testing	50000	5000000						44	0.992
2019-03-16T14:50:45	n0n0t	machine	250000	25000000						3	0.338
2019-05-03T14:19:33	TJAOI	Manual testing	250000	25000000						35	3.944
2021-04-17T03:42:08	GAN	N-34	250000	25000000	53038315068198497675402041	85.455	5	2	1740134595039465	5	0.563

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
2015-04-11T15:44:00	MadPoo	Manual testing	A039F319EFB063__	0.014

PRP results:

date

userid

compid

cofactors

res64

PRP

2021-04-17T03:54:11

mikr

Nitron

53038315068198497675402041

E4D0B08C0294B8__

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 = 200000000 (P-1 stage 2)

B1 = 10000000 (P-1 stage 1)

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

B1 = 534063 (P-1 stage 1)

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

B1 = 320438 (P-1 stage 1)

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

B1 = 131072 (P-1 stage 1)

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

B1 = 65536 (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)

10²

10³

10⁴

10⁵

10⁶

10⁷

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

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: 2022-03-07T09:21:23+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