M1902193 Mersenne number exponent details

is 2 ^1902193 - 1

has 572618 decimal digits

takes 0.103 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	31.3348	69.1176%	8000000	320000000	1.9665	9.7317%	33.3013	72.1230%	3.0054%
PrimeNet	2⁵⁷	0.0101	63.1579%	9000	160000	0.0014	3.0387%	0.0114	64.2774%	1.1195%
GPU72	2⁶¹	0.1615	65.5738%	10000	160000	0.0014	1.7277%	0.1629	66.1686%	0.5948%
Difference	+7	+31.1733	+3.5439%	+7990000	+319840000	+1.9650	+8.0040%	+33.1384	+5.9545%	+5.9545%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1902193	4019946437243639267695249	25	81.733	1056661032093914568 2³ × 3 × 506797 × 86874119231	2020-12-02	506797	86874119231	494,184	372.36	695.39

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2002-08-10T00:00:00	Jocelyn Larouche	v4_computers	20000	160000		-		-	-	0.002	-	-	0.732%
2011-02-10T06:34:00	Carsten Kossendey	leela	105000	1785000		-		-	-	0.015	-	-	2.280%
2011-06-19T08:33:00	kurly	kk	1000000	30000000		-		-	-	0.203	-	-	5.680%
2017-11-24T09:27:44	mikr	S065	8000000	320000000	12	-		-	-	1.966	-	-	9.732%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2011-02-05T00:00:00	GrunwalderGIMP	v4_computers	2¹	2⁵⁶		-	-	0.005	-	-
2011-02-05T00:00:00	GrunwalderGIMP	v4_computers	2⁵⁶	2⁵⁷		-	-	0.005	-	-
2002-01-02T00:00:00	Jocelyn Larouche	v4_computers	2¹	2⁵⁸		-	-	0.020	-	-
2011-02-05T00:00:00	GrunwalderGIMP	v4_computers	2⁵⁷	2⁵⁸		-	-	0.010	-	-
2011-02-05T00:00:00	GrunwalderGIMP	v4_computers	2⁵⁸	2⁵⁹		-	-	0.020	-	-
2011-02-05T00:00:00	GrunwalderGIMP	v4_computers	2⁵⁹	2⁶⁰		-	-	0.040	-	-
2011-02-05T00:00:00	GrunwalderGIMP	v4_computers	2⁶⁰	2⁶¹		-	-	0.081	-	-
2009-05-24T16:06:00	Architects Cubed	i4l_1	2⁶⁰	2⁶¹		-	-	0.081	-	-
2011-01-15T01:36:00	GrunwalderGIMP	GWPrime02	2⁶¹	2⁶²		-	-	0.161	-	-
2011-01-15T05:08:00	GrunwalderGIMP	GWPrime02	2⁶²	2⁶³		-	-	0.516	-	-
2015-05-16T12:25:00	omylist	Manual testing	2⁶³	2⁶⁴		-	-	1.032	-	-
2015-05-16T17:55:00	monst	Manual testing	2⁶⁴	2⁶⁵		-	-	1.964	-	-
2015-08-30T20:42:00	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	3.928	-	-
2017-03-03T09:31:41	Smok_bmv	Manual testing	2⁶⁶	2⁶⁷		-	-	7.857	-	-
2019-04-25T12:32:13	chuenkit	Manual testing	2⁶⁷	2⁶⁸		-	-	15.71	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	18.116 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:	18.116 GHz-days
Estimated T-Level:	24.482

Digits	B1	Complete	FacMiss
20	11000	8.273	0.026%
25	50000	0.748	47.315%
30	250000	0.046	95.489%
35	1000000	0.002	99.788%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		168	11.65
50000	5000000	4019946437243639267695249	4	0.277
50000	6600000		79	6.183

ECM Details

										GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2008-12-04T09:16:00	Architects Cubed	m1_fw	50000	5000000						3	0.208
2009-07-27T14:09:00	James Hintz	06_071509	50000	5000000						3	0.208
2010-11-26T14:46:00	Lukasz Wrobel	cm-3	50000	5000000						3	0.208
2012-10-15T11:33:00	Bud	annan	50000	5000000						3	0.208
2013-11-11T19:08:00	Sara	Sara	50000	5000000						3	0.208
2014-07-25T07:16:00	Sara	Sara	50000	5000000						3	0.208
2015-06-30T08:44:00	Sara	Sara	50000	5000000						3	0.208
2015-12-14T17:32:44	John Burroughs	JohnsTardis	50000	5000000						3	0.208
2016-06-11T03:14:13	Bruce	Desk6	50000	5000000						3	0.208
2016-08-17T07:21:16	Bruce	test	50000	5000000						3	0.208
2017-02-02T12:58:47	Bruce	Desk6	50000	5000000						3	0.208
2017-07-14T13:36:20	Bruce	Desk6	50000	5000000						3	0.208
2017-12-04T11:45:37	Lelikoid	QH	50000	5000000						3	0.208
2018-03-30T21:56:21	Bruce	Desk6	50000	5000000						3	0.208
2018-08-29T08:21:24	Bruce	Desk6	50000	5000000						3	0.208
2019-11-08T05:03:16	monsted	rootweiler	50000	5000000						3	0.208
2019-11-30T03:36:06	Alvin Bunk	i7-Core	50000	5000000						3	0.208
2019-12-03T16:42:35	Keysarecool	Boat_Anchor	50000	5000000						3	0.208
2019-12-08T17:37:03	Claude Portenier	Petit-Idiot	50000	5000000						3	0.208
2019-12-12T12:27:48	mnd9	75211backdoorb	50000	5000000						3	0.208
2019-12-17T02:51:46	George Woltman	colab	50000	5000000						3	0.208
2019-12-23T00:41:47	Nesowa	6700T	50000	5000000						3	0.208
2019-12-28T23:47:25	TheJudger	myECM	50000	5000000						3	0.208
2020-01-03T00:11:38	Chang Chia-Tche	ex-ctcpc	50000	5000000						3	0.208
2020-01-08T20:50:06	Keysarecool	Boat_Anchor	50000	5000000						3	0.208
2020-01-17T02:29:57	EricP	Cannonfodder	50000	5000000						3	0.208
2020-01-22T12:40:37	mnd9	221Rb	50000	5000000						3	0.208
2020-01-29T11:19:10	Keysarecool	Boat_Anchor	50000	5000000						3	0.208
2020-02-07T22:04:48	Keysarecool	Boat_Anchor	50000	5000000						3	0.208
2020-02-15T19:40:48	mnd9	75201b	50000	5000000						3	0.208
2020-02-23T04:57:29	mnd9	75211backdoorb	50000	5000000						3	0.208
2020-03-02T06:50:22	Massimo Cappelli (ik5pwa)	maxlinux_3	50000	5000000						3	0.208
2020-03-07T02:51:46	mnd9	75201b	50000	5000000						3	0.208
2020-03-14T11:47:31	kracker	O0	50000	5000000						3	0.208
2020-03-22T01:35:00	IanGlencross	glenx24	50000	5000000						3	0.208
2020-04-03T10:09:03	mnd9	fb	50000	5000000						3	0.208
2020-04-23T13:23:27	Palantsevich	OfficeB01	50000	5000000						3	0.208
2020-04-26T14:03:55	nordi	sweet16	50000	5000000						3	0.208
2020-05-05T06:42:37	Oliver Kruse	IOS-1	50000	5000000						3	0.208
2020-05-17T01:44:23	mnd9	libproj	50000	5000000						3	0.208
2020-06-03T18:37:07	Keysarecool	HPLaptop	50000	5000000						3	0.208
2020-06-22T13:26:33	mnd9	office2	50000	5000000						3	0.208
2020-07-01T21:22:10	GAN	LMS-04	50000	5000000						3	0.208
2020-07-09T08:48:12	GAN	KL-10	50000	5000000						3	0.208
2020-07-14T14:09:06	Ahmed Azhad	c5.large.az	50000	5000000						3	0.208
2020-07-20T18:12:59	Ahmed Azhad	c5.large.az	50000	5000000						3	0.208
2020-07-27T03:22:35	GAN	LMS-18	50000	5000000						3	0.208
2020-08-04T01:01:32	mnd9	libproj	50000	5000000						3	0.208
2020-08-11T08:13:51	GAN	LMS-03	50000	5000000						3	0.208
2020-10-02T07:06:30	Brett Walker	brain	50000	5000000						7	0.486
2020-10-26T23:57:48	lycorn	colab_DG_1	50000	5000000						7	0.486
2020-10-30T03:21:52	Brett Walker	brain	50000	5000000						7	0.486
2020-12-02T20:53:09	daveward2005	Dave2	50000	5000000	4019946437243639267695249	81.733	4	2	1711930059501405	4	0.277
2021-12-10T12:35:47	TJAOI	Manual testing	50000	6600000						79	6.183

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1999-03-15T00:00:00	ANONYMOUS	v4_computers	99EDF4675B75893E	0.103
2015-07-14T15:04:00	MadPoo	Manual testing	99EDF4675B75893E	0.103

PRP results:

date

userid

compid

cofactors

res64

PRP

2020-12-02T21:15:49

mrh

lanai

4019946437243639267695249

8B919F393820AA25

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 = 8000000, B2 = 320000000 (P-1 stage 2)

B1 = 8000000 (P-1 stage 1)

B1 = 1000000, B2 = 30000000 (P-1 stage 2)

B1 = 1000000 (P-1 stage 1)

B1 = 105000, B2 = 1785000 (P-1 stage 2)

B1 = 105000 (P-1 stage 1)

B1 = 20000, B2 = 160000 (P-1 stage 2)

B1 = 20000 (P-1 stage 1)

10³

10⁴

10⁵

10⁶

10⁷

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

TF factor-bounds graph:

2⁶⁸

2⁶⁷

2⁶⁶

2⁶⁵

2⁶⁴

2⁶³

2⁶²

2⁶¹

2⁶⁰

2⁵⁹

2⁵⁸

2⁵⁷

2⁵⁶

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

Last modified: 2021-12-10T12:35:47+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