M1837967 Mersenne number exponent details

is 2 ^1837967 - 1

has 553284 decimal digits

takes 0.100 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	32.4298	69.1176%	1837967	183796700	0.9244	8.0208%	33.3542	71.5947%	2.4770%
PrimeNet	2⁵⁷	0.0104	63.1579%	8000	150000	0.0012	2.8815%	0.0117	64.2195%	1.0616%
GPU72	2⁶¹	0.1671	65.5738%	9000	140000	0.0013	1.5960%	0.1684	66.1232%	0.5494%
Difference	+7	+32.2627	+3.5439%	+1828967	+183656700	+0.9231	+6.4248%	+33.1858	+5.4714%	+5.4714%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1837967	696438876553682456053961	24	79.204	189459026346414940 2² × 5 × 22441 × 422126969267	2019-12-02	22441	422126969267	118,232	1,809.1	3,379.0

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2011-02-07T12:47:00	Carsten Kossendey	leela	100000	1675000		-		-	-	0.015	-	-	2.211%
2014-05-19T21:00:00	Jocelyn Larouche	Manual testing	134921	134921		-		-	-	0.011	-	-	0.925%
2014-09-22T21:00:00	Jocelyn Larouche	Manual testing	169842	169842		-		-	-	0.013	-	-	1.050%
2015-07-03T22:51:00	mikr	MSI	2780000	91760000		-		-	-	0.600	-	-	7.493%
2018-08-13T11:55:02	Jocelyn Larouche	low 4M	1837967	183796700	12	-		-	-	0.924	-	-	8.021%

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	-	-
2010-04-17T14:28:00	Architects Cubed	a3_lm	2⁶⁰	2⁶¹		-	-	0.084	-	-
2016-02-23T16:28:54	Mark Rose	Manual testing	2⁶¹	2⁶²		-	-	0.167	-	-
2011-01-21T16:11:00	GrunwalderGIMP	Manual testing	2¹	2⁶³		-	-	0.868	-	-
2016-02-23T16:28:54	Mark Rose	Manual testing	2⁶²	2⁶³		-	-	0.534	-	-
2015-04-27T03:38:00	snme2pm1	Manual testing	2⁶³	2⁶⁴		-	-	1.068	-	-
2015-04-27T03:38:00	snme2pm1	Manual testing	2⁶⁴	2⁶⁵		-	-	2.033	-	-
2015-09-05T13:49:00	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	4.066	-	-
2018-01-15T16:18:57	TJAOI	Manual testing	2⁶⁶	2⁶⁷		-	-	8.132	-	-
2019-06-17T12:14:59	TJAOI	Manual testing	2⁶⁷	2⁶⁸		-	-	16.26	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	19.009 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:	19.009 GHz-days
Estimated T-Level:	24.482

Digits	B1	Complete	FacMiss
20	11000	8.517	0.020%
25	50000	0.771	46.237%
30	250000	0.048	95.342%
35	1000000	0.002	99.781%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		60	4.146
50000	5000000	696438876553682456053961	2	0.138
50000	6600000		189	14.72

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2008-10-13T11:31:00	Anton Repko	tethys	50000	5000000						3	0.207
2009-07-25T05:47:00	Conductor	home	50000	5000000						3	0.207
2010-11-16T17:21:00	Lupo	yorick	50000	5000000						3	0.207
2012-06-04T11:49:00	Jacques MOLNE	Crazy_64	50000	5000000						3	0.207
2013-08-27T10:49:00	Chang Chia-Tche	exbpc13	50000	5000000						3	0.207
2014-05-16T06:49:00	Sara	Sara	50000	5000000						3	0.207
2014-11-14T11:08:00	mikr	MSI	50000	5000000						12	0.829
2016-06-01T21:48:21	Bruce	DESK3	50000	5000000						3	0.207
2016-09-08T07:31:09	Bruce	DESK3	50000	5000000						3	0.207
2016-11-15T14:43:05	Chang Chia-Tche	exbpc13	50000	5000000						3	0.207
2017-01-13T21:41:31	Bruce	DESK3	50000	5000000						3	0.207
2017-05-15T10:07:25	Chang Chia-Tche	exbpc13	50000	5000000						3	0.207
2017-12-10T13:34:31	Bruce	DESK3	50000	5000000						3	0.207
2018-02-11T12:26:18	Bruce	DESK3	50000	5000000						3	0.207
2019-11-24T04:56:22	Claude Portenier	Petit-Idiot	50000	5000000						3	0.207
2019-11-25T14:32:34	daveward2005	Davy	50000	5000000						3	0.207
2019-11-28T08:55:08	-Anonymous-		50000	5000000						3	0.207
2019-12-02T11:54:37	mnd9	75202	50000	5000000	696438876553682456053961	79.204	2	2	8521646142184873	2	0.138
2021-05-14T12:09:09	TJAOI	Manual testing	50000	6600000						189	14.72

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1998-12-21T00:00:00	ANONYMOUS	v4_computers	71241AFC06C1AADB	0.100
2015-07-01T17:35:00	MadPoo	Manual testing	71241AFC06C1AADB	0.100

PRP results:

date

userid

compid

cofactors

res64

PRP

2019-12-03T12:52:06

francijezek

BeQuiet

696438876553682456053961

DC00A9299987356D

2019-12-12T03:31:07

mnd9

75201b

696438876553682456053961

DC00A9299987356D

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 = 1837967, B2 = 183796700 (P-1 stage 2)

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

B1 = 2780000 (P-1 stage 1)

B1 = 1837967 (P-1 stage 1)

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

B1 = 169842 (P-1 stage 1)

B1 = 134921 (P-1 stage 1)

B1 = 100000 (P-1 stage 1)

10³

10⁴

10⁵

10⁶

10⁷

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: 2021-05-14T12:09:09+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