M1681991 Mersenne number exponent details

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M1681991

<<<

>>>

is 2 ^1681991 - 1

has 506330 decimal digits

takes 0.079 GHz-days to do one PRP test

Last-known PrimeNet details:

Exponent is not assigned to anyone

factored, 0 LL tests remaining

	Residue	Status
L-L	69BE0F0158E430E4	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	2⁶⁸	35.4371	69.1176%	25000000	568177269660	2,114.0606	20.7571%	2,149.4977	75.5279%	6.4103%
Target	2⁶¹	0.1826	65.5738%	7000	90000	0.0008	1.2557%	0.1834	66.0061%	0.4323%
Difference	+7	+35.2545	+3.5439%	+24993000	+568177179660	+2,114.0599	+19.5014%	+2,149.3143	+9.5219%	+5.9780%

Known prime factors (1 factor, 143.5 bits, 0.00853161% 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
1681991	15779407377086668348816391432770630504092911	44	143.501	4690693165744248437957275464842151505 5 × 11 × 19 × 61 × 23753 × 132607 × 5515723 × 18811409 × 225155317	2022-12-20	18811409	225155317	9.586e+10	2.0509	2.6126

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2011-01-24T11:29:00	Jocelyn Larouche	Manual testing	50000	50000		-		-	-	0.003	-	-	0.487%
2012-02-29T17:10:00	Axon	Manual testing	100000	100000		-		-	-	0.007	-	-	0.764%
2012-02-29T17:15:00	Axon	Manual testing	200000	200000		-		-	-	0.014	-	-	1.128%
2012-02-29T18:10:00	Axon	Manual testing	300000	300000		-		-	-	0.020	-	-	1.383%
2012-02-29T18:13:00	Axon	Manual testing	400000	400000		-		-	-	0.027	-	-	1.584%
2012-02-29T19:11:00	Axon	Manual testing	500000	500000		-		-	-	0.034	-	-	1.751%
2012-02-29T19:13:00	Axon	Manual testing	600000	600000		-		-	-	0.041	-	-	1.895%
2012-02-29T20:10:00	Axon	Manual testing	700000	700000		-		-	-	0.048	-	-	2.021%
2012-02-29T20:13:00	Axon	Manual testing	800000	800000		-		-	-	0.055	-	-	2.135%
2012-02-29T21:11:00	Axon	Manual testing	900000	900000		-		-	-	0.061	-	-	2.238%
2012-02-29T21:14:00	Axon	Manual testing	1000000	1000000		-		-	-	0.068	-	-	2.332%
2012-03-01T06:09:00	Axon	Manual testing	1000000	8000000		-		-	-	0.094	-	-	4.302%
2012-03-01T07:10:00	Axon	Manual testing	1000000	20000000		-		-	-	0.139	-	-	5.199%
2018-01-21T11:09:17	Jocelyn Larouche	low 4M	1681991	20000000	12	-		-	-	0.183	-	-	5.443%
2018-02-06T13:08:09	Jocelyn Larouche	low 4M	1681991	40000000	12	-		-	-	0.257	-	-	6.195%
2018-02-20T12:50:32	Jocelyn Larouche	low 4M	1681991	80000000	12	-		-	-	0.406	-	-	6.956%
2018-06-14T11:36:25	Jocelyn Larouche	low 4M	1681991	168199100	12	-		-	-	0.734	-	-	7.781%
2018-10-16T11:47:55	Jocelyn Larouche	low 4M	1681991	185019010	12	-		-	-	0.796	-	-	7.888%
2022-12-20T21:17:28	Naegi Makoto	5950X	25000000	568177269660			15779407377086668348816391432770630504092911	44	143.501	2,114	0.158	4,228	20.757%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1998-11-14T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁷		-	-	0.011	-	-
2003-03-27T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.023	-	-
2016-02-23T16:28:46	Mark Rose	Manual testing	2⁵⁸	2⁶⁰		-	-	0.068	-	-
2010-04-26T15:50:00	Architects Cubed	m1_76l	2⁶⁰	2⁶¹		-	-	0.091	-	-
2016-02-23T16:28:46	Mark Rose	Manual testing	2⁶¹	2⁶²		-	-	0.183	-	-
2010-09-26T01:51:00	GrunwalderGIMP	Manual testing	2¹	2⁶³		-	-	0.949	-	-
2016-02-23T16:28:46	Mark Rose	Manual testing	2⁶²	2⁶³		-	-	0.584	-	-
2015-05-13T07:35:00	omylist	Manual testing	2⁶³	2⁶⁴		-	-	1.167	-	-
2015-05-14T02:07:00	monst	Manual testing	2⁶⁴	2⁶⁵		-	-	2.221	-	-
2015-10-12T09:32:53	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	4.443	-	-
2017-09-22T15:53:14	TJAOI	Manual testing	2⁶⁶	2⁶⁷		-	-	8.886	-	-
2019-08-16T11:17:52	TJAOI	Manual testing	2⁶⁷	2⁶⁸		-	-	17.77	-	-

ECM factoring results:

Total ECM effort:	16.625 GHz-days
Estimated T-Level:	24.982

Digits	B1	Complete	FacMiss
20	11000	10.769	0.002%
25	50000	0.996	36.919%
30	250000	0.063	93.908%
35	1000000	0.003	99.707%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		280	16.62

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2008-06-14T08:23:00	Scott Kurowski	UW2	50000	5000000						3	0.178
2009-09-16T21:23:00	Mike Lehmann		50000	5000000						3	0.178
2010-06-29T06:02:00	James Hintz	18_051310	50000	5000000						3	0.178
2011-11-01T04:26:00	S36049	Wolle5	50000	5000000						3	0.178
2013-04-03T14:48:00	Chang Chia-Tche	exbpc13	50000	5000000						3	0.178
2013-12-21T18:45:00	Chang Chia-Tche	exbpc13	50000	5000000						3	0.178
2014-08-18T12:24:00	Chang Chia-Tche	exbpc13	50000	5000000						3	0.178
2014-12-02T18:48:00	mikr	MSI	50000	5000000						12	0.712
2016-05-29T03:26:28	Bruce	DESK3	50000	5000000						3	0.178
2016-08-24T13:02:36	Bruce	DESK3	50000	5000000						3	0.178
2016-10-27T03:21:00	Bruce	DESK3	50000	5000000						3	0.178
2016-12-25T07:49:59	Bruce	DESK3	50000	5000000						3	0.178
2017-04-15T02:09:06	ANONYMOUS	Worker	50000	5000000						3	0.178
2017-10-07T13:04:44	Chang Chia-Tche	exbpc13	50000	5000000						3	0.178
2018-01-08T09:10:20	Bruce	DESK3	50000	5000000						3	0.178
2018-10-20T15:04:03	storm5510	7700_Kaby_Lake	50000	5000000						3	0.178
2018-11-08T21:56:06	VictordeHollander	Manual testing	50000	5000000						223	13.24

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1998-12-06T00:00:00	ANONYMOUS	v4_computers	69BE0F0158E430E4	0.079
2015-07-04T19:27:00	MadPoo	Manual testing	69BE0F0158E430E4	0.079

PRP results:

date

userid

compid

cofactors

res64

PRP

2022-12-20T21:20:53

Naegi Makoto

5950X

15779407377086668348816391432770630504092911

E087F70307949FA0

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 = 25000000, B2 = 568177269660 (P-1 stage 2)

B1 = 25000000 (P-1 stage 1)

B1 = 1681991, B2 = 185019010 (P-1 stage 2)

B1 = 1681991, B2 = 168199100 (P-1 stage 2)

B1 = 1681991, B2 = 80000000 (P-1 stage 2)

B1 = 1681991, B2 = 40000000 (P-1 stage 2)

B1 = 1681991, B2 = 20000000 (P-1 stage 2)

B1 = 1000000, B2 = 20000000 (P-1 stage 2)

B1 = 1681991 (P-1 stage 1)

B1 = 1000000, B2 = 8000000 (P-1 stage 2)

B1 = 1000000 (P-1 stage 1)

B1 = 900000 (P-1 stage 1)

B1 = 800000 (P-1 stage 1)

B1 = 700000 (P-1 stage 1)

B1 = 600000 (P-1 stage 1)

B1 = 500000 (P-1 stage 1)

B1 = 400000 (P-1 stage 1)

B1 = 300000 (P-1 stage 1)

B1 = 200000 (P-1 stage 1)

B1 = 100000 (P-1 stage 1)

B1 = 50000 (P-1 stage 1)

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

10¹²

TF factor-bounds graph:

2⁶⁸

2⁶⁷

2⁶⁶

2⁶⁵

2⁶⁴

2⁶³

2⁶²

2⁶¹

2⁶⁰

2⁵⁸

2⁵⁷

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

2¹¹⁰

2¹²⁰

2¹³⁰

2¹⁴⁰

2¹⁵⁰

Last modified: 2022-12-20T21:20:53+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