M2131361 Mersenne number exponent details

is 2 ^2131361 - 1

has 641604 decimal digits

takes 0.140 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	27.9656	67.6471%	2500000	125000000	0.8746	7.9100%	28.8403	70.2062%	2.5591%
PrimeNet	2⁵⁸	0.0180	62.0690%	9000	170000	0.0017	2.7293%	0.0197	63.1042%	1.0352%
GPU72	2⁶²	0.2882	64.5161%	10000	150000	0.0017	1.4863%	0.2899	65.0435%	0.5274%
Difference	+6	+27.6774	+3.1309%	+2490000	+124850000	+0.8730	+6.4237%	+28.5504	+5.1627%	+5.1627%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2131361	10373065398361854238577	23	73.135	2433436991284408 2³ × 19 × 71287 × 224577467	2020-07-18	71287	224577467	1,322.6	1.1729	2.1787

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2011-01-12T23:59:00	Jocelyn Larouche	Manual testing	50000	50000		-		-	-	0.005	-	-	0.512%
2011-01-22T08:25:00	James Heinrich	i7-920	140000	3045000		-		-	-	0.028	-	-	2.779%
2016-06-29T03:46:57	Jocelyn Larouche	Manual testing	210000	6090000	12	-		-	-	0.051	-	-	3.464%
2017-08-19T15:19:16	Jocelyn Larouche	low 4M	420000	4200000	6	-		-	-	0.060	-	-	3.511%
2017-08-30T00:32:09	Jocelyn Larouche	low 4M	504000	5040000	6	-		-	-	0.072	-	-	3.737%
2017-09-24T02:12:39	mikr	MSI	2500000	125000000	12	-		-	-	0.875	-	-	7.910%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1997-11-12T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁷		-	-	0.009	-	-
1999-01-29T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.018	-	-
2016-02-23T16:29:06	Mark Rose	Manual testing	2⁵⁸	2⁶⁰		-	-	0.054	-	-
2009-01-05T05:08:00	Sturle Sunde	celair.ifi	2⁶⁰	2⁶¹		-	-	0.072	-	-
2012-04-14T21:49:00	Sebastian Hornbostel	Manual testing	2⁶¹	2⁶²		-	-	0.144	-	-
2013-09-07T11:35:00	ramgeis	Manual testing	2⁶²	2⁶³		-	-	0.461	-	-
2015-03-15T12:13:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.921	-	-
2015-03-15T12:13:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.753	-	-
2015-12-27T16:49:12	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	3.506	-	-
2016-10-29T15:24:08	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	7.012	-	-
2019-04-29T13:20:35	TJAOI	Manual testing	2⁶⁷	2⁶⁸		-	-	14.02	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	8.526 GHz-days
Estimated T-Level:	21.786

Digits	B1	Curves	Complete	FacMiss
20	11000	100 / 100	1.000	36.603%
25	50000	100 / 280	0.357	69.923%

New Calculation Method

Total ECM effort:	8.526 GHz-days
Estimated T-Level:	21.786

Digits	B1	Complete	FacMiss
20	11000	3.226	3.972%
25	50000	0.292	74.711%
30	250000	0.018	98.221%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		99	8.440
50000	5000000	10373065398361854238577	1	0.085

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-01-02T19:38:00	Nathan Slaven	q6600	50000	5000000						3	0.256
2009-11-20T02:18:00	James Hintz	ryan	50000	5000000						3	0.256
2011-08-01T19:35:00	Csaba Vágó	timigep	50000	5000000						3	0.256
2013-04-20T14:38:00	OS1	L3	50000	5000000						3	0.256
2014-12-04T14:09:00	AdolfNor	PC4	50000	5000000						3	0.256
2015-08-11T16:06:00	guru	w1	50000	5000000						3	0.256
2016-02-25T03:04:30	arnaud	PORTABLE08	50000	5000000						3	0.256
2016-06-10T04:50:49	Bruce	Desk6	50000	5000000						3	0.256
2016-08-31T11:17:19	Bruce	test	50000	5000000						3	0.256
2017-03-06T14:47:41	Bruce	Desk6	50000	5000000						3	0.256
2017-09-18T01:46:33	Bruce	Desk6	50000	5000000						3	0.256
2018-02-01T08:27:10	Bruce	Desk6	50000	5000000						3	0.256
2018-07-16T11:53:57	Bruce	Desk6	50000	5000000						3	0.256
2019-09-08T05:29:28	Chang Chia-Tche	ex-ctcpc	50000	5000000						3	0.256
2020-01-19T20:04:15	Yuji HASEGAWA	sx1w7	50000	5000000						3	0.256
2020-02-02T14:35:23	David_McCann	i5	50000	5000000						3	0.256
2020-02-12T15:03:48	mnd9	office2	50000	5000000						3	0.256
2020-02-16T08:32:31	S04803	lfmcal	50000	5000000						3	0.256
2020-02-18T00:57:03	Keysarecool	Boat_Anchor	50000	5000000						3	0.256
2020-02-25T22:40:22	Nesowa	entropy_generator_2	50000	5000000						3	0.256
2020-03-03T04:15:52	Keysarecool	HPLaptop	50000	5000000						3	0.256
2020-03-09T09:43:39	mnd9	50869b	50000	5000000						3	0.256
2020-03-17T07:31:56	mnd9	75201b	50000	5000000						3	0.256
2020-03-26T23:59:30	MarkS	laptop64	50000	5000000						3	0.256
2020-04-07T23:37:02	mnd9	eileen	50000	5000000						3	0.256
2020-04-21T13:46:01	mnd9	office2	50000	5000000						3	0.256
2020-04-28T20:39:43	EricP	Cannonfodder	50000	5000000						3	0.256
2020-05-09T17:09:27	daveward2005	MW	50000	5000000						3	0.256
2020-05-23T14:59:27	mnd9	office2	50000	5000000						3	0.256
2020-06-12T02:33:25	mnd9	50871b	50000	5000000						3	0.256
2020-06-27T06:41:19	Sergey Nosov	TS140-02	50000	5000000						3	0.256
2020-07-04T13:24:59	MarkS	laptop64	50000	5000000						3	0.256
2020-07-11T10:06:33	mnd9	libproj	50000	5000000						3	0.256
2020-07-17T17:57:24	GAN	KA-AC	50000	5000000	10373065398361854238577	73.135	1	2	6532403970795200	1	0.085

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1997-11-12T00:00:00	ANONYMOUS	v4_computers	CD4836F5EBBCBF29	0.140
1999-02-07T00:00:00	ANONYMOUS	v4_computers	CD4836F5EBBCBF29	0.140
2018-04-05T19:32:56	kkmrkkblmbrbk	old	CD4836F5EBBCBF29	0.140

PRP results:

date

userid

compid

cofactors

res64

PRP

2020-07-17T18:21:12

ATH

ec2-PRPCF

10373065398361854238577

AA225866B94DD4A9

2020-07-17T20:19:20

oodaira

com2

10373065398361854238577

AA225866B94DD4A9

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 = 2500000, B2 = 125000000 (P-1 stage 2)

B1 = 2500000 (P-1 stage 1)

B1 = 504000, B2 = 5040000 (P-1 stage 2)

B1 = 420000, B2 = 4200000 (P-1 stage 2)

B1 = 210000, B2 = 6090000 (P-1 stage 2)

B1 = 504000 (P-1 stage 1)

B1 = 420000 (P-1 stage 1)

B1 = 140000, B2 = 3045000 (P-1 stage 2)

B1 = 210000 (P-1 stage 1)

B1 = 140000 (P-1 stage 1)

B1 = 50000 (P-1 stage 1)

10³

10⁴

10⁵

10⁶

10⁷

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

TF factor-bounds graph:

2⁶⁸

2⁶⁷

2⁶⁶

2⁶⁵

2⁶⁴

2⁶³

2⁶²

2⁶¹

2⁶⁰

2⁵⁸

2⁵⁷

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

Last modified: 2020-07-18T00:11:59+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