M1816051 Mersenne number exponent details

is 2 ^1816051 - 1

has 546686 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	32.8211	69.1176%	1816051	181605100	0.9134	7.9882%	33.7345	71.5846%	2.4670%
PrimeNet	2⁵⁷	0.0106	63.1579%	8000	150000	0.0012	2.8750%	0.0118	64.2171%	1.0592%
GPU72	2⁶¹	0.1691	65.5738%	9000	130000	0.0012	1.5572%	0.1704	66.1099%	0.5361%
Difference	+7	+32.6520	+3.5439%	+1807051	+181475100	+0.9122	+6.4310%	+33.5642	+5.4747%	+5.4747%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1816051	1489729824434788064332828313	28	90.267	410156384494374900356 2² × 13 × 3181 × 2479604771687513	2020-06-18	3181	2479604771687513	197,124,399	10,626,966	19,848,213

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2011-01-31T18:29:00	henryzz		100000	10000000		-		-	-	0.050	-	-	3.241%
2014-05-13T21:11:00	Jocelyn Larouche	Manual testing	135343	135343		-		-	-	0.011	-	-	0.924%
2014-09-22T21:00:00	Jocelyn Larouche	Manual testing	170686	170686		-		-	-	0.013	-	-	1.050%
2015-05-24T16:28:00	mikr	MSI	2780000	91760000		-		-	-	0.600	-	-	7.484%
2018-09-10T11:51:54	Jocelyn Larouche	low 4M	1816051	181605100	12	-		-	-	0.913	-	-	7.988%

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	-	-
2016-02-23T16:28:53	Mark Rose	Manual testing	2⁵⁸	2⁶⁰		-	-	0.063	-	-
2010-04-17T18:46:00	Architects Cubed	a3_bu2	2⁶⁰	2⁶¹		-	-	0.085	-	-
2011-02-03T13:02:00	Matteo2D		2⁶¹	2⁶²		-	-	0.169	-	-
2011-02-05T00:00:00	ANONYMOUS	v4_computers	2⁶²	2⁶³		-	-	0.541	-	-
2011-02-04T16:50:00	Matteo2D		2⁶²	2⁶³		-	-	0.541	-	-
2015-04-23T05:08:00	snme2pm1	Manual testing	2⁶³	2⁶⁴		-	-	1.081	-	-
2015-04-23T05:08:00	snme2pm1	Manual testing	2⁶⁴	2⁶⁵		-	-	2.057	-	-
2015-09-02T13:37:00	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	4.115	-	-
2018-03-19T15:07:58	TJAOI	Manual testing	2⁶⁶	2⁶⁷		-	-	8.230	-	-
2019-06-24T09:36:04	TJAOI	Manual testing	2⁶⁷	2⁶⁸		-	-	16.46	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	17.321 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:	17.321 GHz-days
Estimated T-Level:	24.482

Digits	B1	Complete	FacMiss
20	11000	8.097	0.030%
25	50000	0.732	48.105%
30	250000	0.045	95.594%
35	1000000	0.002	99.794%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		249	17.18
50000	5000000	1489729824434788064332828313	2	0.138

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2008-09-19T09:18:00	Scott Kurowski	UW1	50000	5000000						3	0.207
2009-07-15T15:45:00	James Hintz	17_071409	50000	5000000						3	0.207
2014-05-14T10:12:00	Chang Chia-Tche	exbpc13	50000	5000000						3	0.207
2014-05-14T11:14:00	Chang Chia-Tche	exbpc13	50000	5000000						3	0.207
2014-05-16T13:03:00	Lukasz Wrobel	w1	50000	5000000						3	0.207
2014-06-11T19:20:00	S36049	Wolle4	50000	5000000						3	0.207
2014-09-07T22:15:00	mikr	MSI	50000	5000000						12	0.828
2016-05-23T11:11:38	Bruce	DESK3	50000	5000000						3	0.207
2016-08-24T06:47:47	Bruce	DESK3	50000	5000000						3	0.207
2016-11-03T01:01:52	Bruce	DESK3	50000	5000000						3	0.207
2017-01-04T09:47:19	Bruce	DESK3	50000	5000000						3	0.207
2017-04-26T00:34:16	ANONYMOUS	Worker	50000	5000000						3	0.207
2017-11-21T17:07:25	Bruce	DESK3	50000	5000000						3	0.207
2018-01-30T04:46:24	Bruce	DESK3	50000	5000000						3	0.207
2019-11-20T20:08:10	Sergey Nosov	TS140-02	50000	5000000						3	0.207
2019-11-23T12:41:12	mnd9	dlounge	50000	5000000						3	0.207
2019-11-25T18:15:35	penlu	grizzly	50000	5000000						3	0.207
2019-11-27T18:13:48	Alvin Bunk	i7-Core	50000	5000000						3	0.207
2019-12-01T13:44:30	Bommer	3770K	50000	5000000						3	0.207
2019-12-05T06:39:43	J.R. Allen	lapacer	50000	5000000						3	0.207
2019-12-10T11:08:24	arnaud	PORTABLE08	50000	5000000						3	0.207
2019-12-14T06:54:07	J.R. Allen	lapdell	50000	5000000						3	0.207
2020-06-17T10:17:31	daveward2005	Davy	50000	5000000						3	0.207
2020-06-17T15:20:29	GAN	PG-HP	50000	5000000						3	0.207
2020-06-17T17:07:54	Travis Glenn Russo	ROG-4900HS	50000	5000000						3	0.207
2020-06-17T23:58:39	IanGlencross	glenx24	50000	5000000						3	0.207
2020-06-18T00:38:02	mnd9	kitchen	50000	5000000						3	0.207
2020-06-18T00:54:26	mnd9	office2	50000	5000000						3	0.207
2020-06-18T03:23:18	lycorn	colab_ES	50000	5000000						3	0.207
2020-06-18T07:18:15	mnd9	touchdown	50000	5000000						3	0.207
2020-06-18T09:30:52	IanGlencross	glenx24	50000	5000000						3	0.207
2020-06-18T12:13:58	mnd9	touchdown	50000	5000000	1489729824434788064332828313	90.267	2	2	1142776918160583	2	0.138
2020-06-18T15:17:16	mnd9	office2	50000	5000000						3	0.207
2020-06-19T11:19:00	Yxinity	Olga	50000	5000000						3	0.207
2020-06-20T09:51:11	GAN	LMS-03	50000	5000000						3	0.207
2021-03-05T18:09:51	TJAOI	Manual testing	50000	5000000						138	9.52

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1998-12-21T00:00:00	ANONYMOUS	v4_computers	6179A5ADF68CDE64	0.099
2015-07-18T18:31:00	MadPoo	Manual testing	6179A5ADF68CDE64	0.099

PRP results:

date

userid

compid

cofactors

res64

PRP

2020-06-18T12:29:55

mnd9

mnd

1489729824434788064332828313

F6EE01138C83BEC3

2020-06-18T14:07:33

CrypticClue

cruncher

1489729824434788064332828313

F6EE01138C83BEC3

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 = 1816051, B2 = 181605100 (P-1 stage 2)

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

B1 = 2780000 (P-1 stage 1)

B1 = 1816051 (P-1 stage 1)

B1 = 100000, B2 = 10000000 (P-1 stage 2)

B1 = 170686 (P-1 stage 1)

B1 = 135343 (P-1 stage 1)

B1 = 100000 (P-1 stage 1)

10²

10³

10⁴

10⁵

10⁶

10⁷

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

10¹²

10¹³

10¹⁴

10¹⁵

10¹⁶

TF factor-bounds graph:

2⁶⁸

2⁶⁷

2⁶⁶

2⁶⁵

2⁶⁴

2⁶³

2⁶²

2⁶¹

2⁶⁰

2⁵⁸

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

Last modified: 2021-03-05T18:09:51+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