M1810561 Mersenne number exponent details

is 2 ^1810561 - 1

has 545034 decimal digits

takes 0.098 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	32.9207	69.1176%	1810561	181056100	0.9106	7.9800%	33.8313	71.5821%	2.4644%
PrimeNet	2⁵⁷	0.0106	63.1579%	8000	150000	0.0012	2.8733%	0.0118	64.2165%	1.0586%
GPU72	2⁶¹	0.1697	65.5738%	9000	130000	0.0012	1.5562%	0.1709	66.1095%	0.5357%
Difference	+7	+32.7510	+3.5439%	+1801561	+180926100	+0.9094	+6.4238%	+33.6604	+5.4725%	+5.4725%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1810561	12000431416426228695817	23	73.346	3314009143140228 2² × 3⁵ × 13 × 262267263623	2019-11-22	243	262267263623	1,794.7	1,124.0	2,099.3

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2011-02-07T12:43:00	Carsten Kossendey	leela	100000	1650000		-		-	-	0.015	-	-	2.198%
2014-05-12T10:21:00	Jocelyn Larouche	Manual testing	135450	135450		-		-	-	0.011	-	-	0.924%
2014-09-20T22:31:00	Jocelyn Larouche	Manual testing	170900	170900		-		-	-	0.013	-	-	1.051%
2015-05-14T05:58:00	mikr	MSI	2780000	91760000		-		-	-	0.600	-	-	7.482%
2018-09-20T11:55:03	Jocelyn Larouche	low 4M	1810561	181056100	12	-		-	-	0.911	-	-	7.980%

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		-	-	0.064	-	-
2010-04-17T14:28:00	Architects Cubed	a3_bu2	2⁶⁰	2⁶¹		-	-	0.085	-	-
2016-02-23T16:28:53	Mark Rose	Manual testing	2⁶¹	2⁶²		-	-	0.170	-	-
2011-01-21T16:10:00	GrunwalderGIMP	Manual testing	2¹	2⁶³		-	-	0.882	-	-
2016-02-23T16:28:53	Mark Rose	Manual testing	2⁶²	2⁶³		-	-	0.542	-	-
2015-04-22T10:38:00	snme2pm1	Manual testing	2⁶³	2⁶⁴		-	-	1.084	-	-
2015-04-22T10:38:00	snme2pm1	Manual testing	2⁶⁴	2⁶⁵		-	-	2.064	-	-
2015-09-01T08:49:00	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	4.127	-	-
2018-04-16T13:13:01	TJAOI	Manual testing	2⁶⁶	2⁶⁷		-	-	8.255	-	-
2019-07-17T09:51:53	TJAOI	Manual testing	2⁶⁷	2⁶⁸		-	-	16.51	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	19.034 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:	19.034 GHz-days
Estimated T-Level:	24.482

Digits	B1	Complete	FacMiss
20	11000	8.533	0.020%
25	50000	0.773	46.170%
30	250000	0.048	95.333%
35	1000000	0.002	99.781%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		54	3.725
50000	5000000	12000431416426228695817	1	0.069
50000	6600000		196	15.24

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2008-09-19T20:02:00	Scott Kurowski	UW1	50000	5000000						3	0.207
2009-10-09T16:13:00	Samoflan	Parker	50000	5000000						3	0.207
2010-10-26T14:29:00	Lackó	Iroda_Laci	50000	5000000						3	0.207
2012-04-10T18:32:00	S36049	Wolle5	50000	5000000						3	0.207
2013-07-19T21:19:00	Chang Chia-Tche	exbpc13	50000	5000000						3	0.207
2014-04-06T11:34:00	Sara	Sara	50000	5000000						3	0.207
2014-08-19T22:23:00	mikr	MSI	50000	5000000						12	0.828
2016-05-21T12:56:08	Chang Chia-Tche	exbpc13	50000	5000000						3	0.207
2016-08-20T18:50:46	Bruce	DESK3	50000	5000000						3	0.207
2016-10-30T06:18:09	Bruce	DESK3	50000	5000000						3	0.207
2017-01-01T17:23:19	Bruce	DESK3	50000	5000000						3	0.207
2017-04-23T04:40:16	ANONYMOUS	Worker	50000	5000000						3	0.207
2017-11-18T15:08:15	Bruce	DESK3	50000	5000000						3	0.207
2018-01-27T01:12:04	Bruce	DESK3	50000	5000000						3	0.207
2019-11-20T06:37:52	Sergey Nosov	TS140-02	50000	5000000						3	0.207
2019-11-22T22:35:02	mnd9	dlounge	50000	5000000	12000431416426228695817	73.346	1	2	7648137141925032	1	0.069
2021-02-12T10:31:26	TJAOI	Manual testing	50000	6600000						196	15.24

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1999-01-02T00:00:00	ANONYMOUS	v4_computers	93C61F18A4279784	0.098
2015-07-06T20:16:00	MadPoo	Manual testing	93C61F18A4279784	0.098

PRP results:

date

userid

compid

cofactors

res64

PRP

2019-11-23T13:31:32

Niels_Mache_Nextcloud

SuperDry-X

12000431416426228695817

4DBC947FBC1F14B8

2019-11-24T10:25:41

GAN

12000431416426228695817

4DBC947FBC1F14B8

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 = 1810561, B2 = 181056100 (P-1 stage 2)

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

B1 = 2780000 (P-1 stage 1)

B1 = 1810561 (P-1 stage 1)

B1 = 100000, B2 = 1650000 (P-1 stage 2)

B1 = 170900 (P-1 stage 1)

B1 = 135450 (P-1 stage 1)

B1 = 100000 (P-1 stage 1)

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

10¹²

TF factor-bounds graph:

2⁶⁸

2⁶⁷

2⁶⁶

2⁶⁵

2⁶⁴

2⁶³

2⁶²

2⁶¹

2⁶⁰

2⁵⁸

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

Last modified: 2021-02-12T10:31:26+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