M1831681 Mersenne number exponent details

is 2 ^1831681 - 1

has 551391 decimal digits

takes 0.099 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	2⁶⁸	32.5411	69.1176%	1831681	183168100	0.9212	8.0115%	33.4623	71.5918%	2.4741%
PrimeNet	2⁵⁷	0.0105	63.1579%	8000	150000	0.0012	2.8796%	0.0117	64.2188%	1.0609%
GPU72	2⁶¹	0.1677	65.5738%	9000	140000	0.0013	1.5949%	0.1690	66.1228%	0.5491%
Difference	+7	+32.3734	+3.5439%	+1822681	+183028100	+0.9200	+6.4166%	+33.2934	+5.4690%	+5.4690%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1831681	539214926691046103249	21	68.869	147191275852904 2³ × 19 × 409 × 2367637303	2019-12-04	409	2367637303	63.370	10.147	18.952

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2002-11-09T00:00:00	ANONYMOUS	v4_computers	25000	437500		-		-	-	0.004	-	-	1.076%
2011-02-10T06:33:00	Carsten Kossendey	leela	100000	1675000		-		-	-	0.015	-	-	2.210%
2014-05-19T21:00:00	Jocelyn Larouche	Manual testing	135041	135041		-		-	-	0.011	-	-	0.924%
2014-09-22T21:00:00	Jocelyn Larouche	Manual testing	170082	170082		-		-	-	0.013	-	-	1.050%
2015-06-22T08:08:00	mikr	MSI	2780000	91760000		-		-	-	0.600	-	-	7.490%
2018-08-17T12:06:12	Jocelyn Larouche	low 4M	1831681	93415731	12	-		-	-	0.537	-	-	7.249%
2018-09-10T11:52:00	Jocelyn Larouche	low 4M	1831681	183168100	12	-		-	-	0.921	-	-	8.011%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2003-01-16T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.021	-	-
2016-02-23T16:28:54	Mark Rose	Manual testing	2⁵⁸	2⁶⁰		-	-	0.063	-	-
2010-04-16T12:29:00	Architects Cubed	a3_lm	2⁶⁰	2⁶¹		-	-	0.084	-	-
2016-02-23T16:28:54	Mark Rose	Manual testing	2⁶¹	2⁶²		-	-	0.168	-	-
2011-01-21T16:10:00	GrunwalderGIMP	Manual testing	2¹	2⁶³		-	-	0.871	-	-
2016-02-23T16:28:54	Mark Rose	Manual testing	2⁶²	2⁶³		-	-	0.536	-	-
2015-04-26T11:10:00	snme2pm1	Manual testing	2⁶³	2⁶⁴		-	-	1.072	-	-
2015-04-26T11:10:00	snme2pm1	Manual testing	2⁶⁴	2⁶⁵		-	-	2.040	-	-
2015-09-04T17:59:00	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	4.080	-	-
2018-03-19T15:07:57	TJAOI	Manual testing	2⁶⁶	2⁶⁷		-	-	8.159	-	-
2019-07-01T11:11:03	TJAOI	Manual testing	2⁶⁷	2⁶⁸		-	-	16.32	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	18.983 GHz-days
Estimated T-Level:	24.482

Digits	B1	Curves	Complete	FacMiss
20	11000	251 / 100	2.510	8.025%
25	50000	251 / 280	0.896	40.737%

New Calculation Method

Total ECM effort:	18.983 GHz-days
Estimated T-Level:	24.482

Digits	B1	Complete	FacMiss
20	11000	8.513	0.020%
25	50000	0.771	46.257%
30	250000	0.048	95.345%
35	1000000	0.002	99.781%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		63	4.352
50000	5000000	539214926691046103249	1	0.069
50000	6600000		187	14.56

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-04-05T16:20:00	James Hintz	09_060902	50000	5000000						3	0.207
2009-07-16T17:03:00	James Hintz	05_071509	50000	5000000						3	0.207
2010-11-12T22:48:00	Chang Chia-Tche	sekhmet	50000	5000000						3	0.207
2012-05-26T21:41:00	Chang Chia-Tche	sekhmet	50000	5000000						3	0.207
2013-08-19T17:56:00	Chang Chia-Tche	exbpc13	50000	5000000						3	0.207
2014-05-12T19:21:00	Sara	Sara	50000	5000000						3	0.207
2014-10-26T15:34:00	mikr	MSI	50000	5000000						12	0.829
2016-05-30T15:33:22	Dennis Schreiber	z800	50000	5000000						3	0.207
2016-09-04T03:22:48	Bruce	DESK3	50000	5000000						3	0.207
2016-11-12T17:49:02	Bruce	DESK3	50000	5000000						3	0.207
2017-01-10T23:13:30	Bruce	DESK3	50000	5000000						3	0.207
2017-05-04T02:27:01	Chang Chia-Tche	exbpc13	50000	5000000						3	0.207
2017-12-05T08:42:22	Bruce	DESK3	50000	5000000						3	0.207
2018-02-08T01:22:36	Bruce	DESK3	50000	5000000						3	0.207
2019-11-22T22:20:39	IanGlencross	glenx24	50000	5000000						3	0.207
2019-11-25T06:00:11	arnaud	CHAMOT06	50000	5000000						3	0.207
2019-11-27T08:22:07	IanGlencross	glenx24	50000	5000000						3	0.207
2019-12-01T10:05:59	nranks	wlaptop	50000	5000000						3	0.207
2019-12-04T13:55:45	daveward2005	Davy	50000	5000000	539214926691046103249	68.869	1	2		1	0.069
2021-04-23T12:19:39	TJAOI	Manual testing	50000	6600000						187	14.56

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1998-12-13T00:00:00	slaur	v4_computers	3AD24165AB6FB249	0.099
1999-01-29T00:00:00	slaur	v4_computers	3AD24165AB6FB249	0.099
2002-11-09T00:00:00	ANONYMOUS	v4_computers	3AD24165AB6FB249	0.099
2016-04-30T09:11:14	kkmrkkblmbrbk	old	3AD24165AB6FB249	0.099

PRP results:

date

userid

compid

cofactors

res64

PRP

2019-12-05T13:16:55

Yuji HASEGAWA

vj20a

539214926691046103249

4D494D26F3AE240D

2019-12-06T12:31:56

marssystems

SYSTEM01

539214926691046103249

4D494D26F3AE240D

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 = 1831681, B2 = 183168100 (P-1 stage 2)

B1 = 2780000, B2 = 91760000 (P-1 stage 2)

B1 = 1831681, B2 = 93415731 (P-1 stage 2)

B1 = 2780000 (P-1 stage 1)

B1 = 1831681 (P-1 stage 1)

B1 = 100000, B2 = 1675000 (P-1 stage 2)

B1 = 170082 (P-1 stage 1)

B1 = 135041 (P-1 stage 1)

B1 = 100000 (P-1 stage 1)

B1 = 25000, B2 = 437500 (P-1 stage 2)

B1 = 25000 (P-1 stage 1)

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

TF factor-bounds graph:

2⁶⁸

2⁶⁷

2⁶⁶

2⁶⁵

2⁶⁴

2⁶³

2⁶²

2⁶¹

2⁶⁰

2⁵⁸

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

Last modified: 2021-04-23T12:19:39+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