M1939909 Mersenne number exponent details

is 2 ^1939909 - 1

has 583971 decimal digits

takes 0.105 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	30.7256	69.1176%	8000000	320000000	1.9665	9.7485%	32.6921	72.1282%	3.0106%
PrimeNet	2⁵⁸	0.0198	63.7931%	8000	140000	0.0012	2.4643%	0.0210	64.6853%	0.8922%
GPU72	2⁶²	0.3167	66.1290%	8000	90000	0.0010	1.1518%	0.3177	66.5192%	0.3901%
Difference	+6	+30.4089	+2.9886%	+7992000	+319910000	+1.9655	+8.5967%	+32.3744	+5.6090%	+5.6090%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1939909	303757575480788269129	21	68.041	78291707363796 2² × 3 × 53 × 123100168811	2020-01-29	53	123100168811	35.368	527.58	985.37

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2011-11-14T19:32:00	kurly	Manual testing	1000000	30000000		-		-	-	0.203	-	-	5.692%
2018-01-27T10:55:55	Jocelyn Larouche	low 4M	1939909	30000000	12	-		-	-	0.273	-	-	6.043%
2018-02-06T08:28:49	mikr	S067	8000000	320000000	12	-		-	-	1.966	-	-	9.748%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1997-12-30T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁷		-	-	0.010	-	-
1998-02-19T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁷		-	-	0.010	-	-
1998-02-24T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁷		-	-	0.010	-	-
1998-03-03T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁷		-	-	0.010	-	-
1998-03-17T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁷		-	-	0.010	-	-
1998-12-21T00:00:00	bezahar	v4_computers	2¹	2⁵⁸		-	-	0.020	-	-
2016-02-23T16:28:59	Mark Rose	Manual testing	2⁵⁸	2⁶⁰		-	-	0.059	-	-
2010-01-29T08:34:00	S485122	USB-W	2⁶⁰	2⁶¹		-	-	0.079	-	-
2016-02-23T16:28:59	Mark Rose	Manual testing	2⁶¹	2⁶²		-	-	0.158	-	-
2011-08-27T22:21:00	GrunwalderGIMP	Manual testing	2¹	2⁶³		-	-	0.823	-	-
2016-02-23T16:28:59	Mark Rose	Manual testing	2⁶²	2⁶³		-	-	0.506	-	-
2015-05-07T07:03:00	lycorn	Manual testing	2⁶³	2⁶⁴		-	-	1.012	-	-
2015-05-07T07:03:00	lycorn	Manual testing	2⁶⁴	2⁶⁵		-	-	1.926	-	-
2015-09-05T13:49:00	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	3.852	-	-
2017-12-04T13:35:48	TJAOI	Manual testing	2⁶⁶	2⁶⁷		-	-	7.704	-	-
2019-05-11T00:32:09	chuenkit	Manual testing	2⁶⁷	2⁶⁸		-	-	15.41	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	19.885 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:	19.885 GHz-days
Estimated T-Level:	24.482

Digits	B1	Complete	FacMiss
20	11000	8.698	0.017%
25	50000	0.775	46.065%
30	250000	0.048	95.313%
35	1000000	0.002	99.779%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		75	5.215
50000	5000000	303757575480788269129	2	0.139
50000	7500000		174	14.53

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2008-11-17T12:26:00	Lars Fricke	M2008	50000	5000000						3	0.209
2009-08-12T10:52:00	Piepen	T41-2000	50000	5000000						3	0.209
2011-01-02T20:28:00	Lupo	yorick	50000	5000000						3	0.209
2012-11-19T21:36:00	Brian V.	dxl5420	50000	5000000						3	0.209
2013-12-17T20:17:00	arnaud	srv-630	50000	5000000						3	0.209
2015-04-07T11:29:00	arnaud	CHAMOT22	50000	5000000						3	0.209
2015-10-14T19:20:42	Chris Smith	starcraft2	50000	5000000						3	0.209
2016-05-17T15:51:28	Marcelo Ellmann	mammy	50000	5000000						3	0.209
2016-06-23T00:57:43	Jason U	Server7	50000	5000000						3	0.209
2016-09-25T00:34:30	Bruce	Desk6	50000	5000000						3	0.209
2017-06-01T23:37:58	Bruce	Desk6	50000	5000000						3	0.209
2017-10-01T07:08:54	Bruce	Desk6	50000	5000000						3	0.209
2017-12-30T00:17:34	alphaLONE	7ubuSTEC	50000	5000000						3	0.209
2018-05-17T10:18:54	Bruce	Desk6	50000	5000000						3	0.209
2019-04-11T11:19:35	Chang Chia-Tche	ex-ctcpc	50000	5000000						3	0.209
2019-12-03T15:25:27	Alvin Bunk	i7-Core	50000	5000000						3	0.209
2019-12-07T08:41:53	George Woltman	colab	50000	5000000						3	0.209
2019-12-12T05:08:05	Idgo	Pentium_Desktop	50000	5000000						3	0.209
2019-12-17T08:55:19	mnd9	75211cornerb	50000	5000000						3	0.209
2019-12-23T10:25:28	mnd9	50871b	50000	5000000						3	0.209
2019-12-28T19:08:56	TheJudger	myECM	50000	5000000						3	0.209
2020-01-02T08:11:33	TheJudger	myECM	50000	5000000						3	0.209
2020-01-09T02:26:56	Nesowa	6700T	50000	5000000						3	0.209
2020-01-16T15:47:02	EricP	Cannonfodder	50000	5000000						3	0.209
2020-01-22T15:52:24	IEFBR14	MK1	50000	5000000						3	0.209
2020-01-29T09:09:13	mnd9	27016b	50000	5000000	303757575480788269129	68.041	2	2	1979007775881254	2	0.139
2022-03-24T12:31:06	TJAOI	Manual testing	50000	7500000						174	14.53

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1998-12-21T00:00:00	bezahar	v4_computers	2A69913940794CAE	0.105
2015-06-27T00:54:00	MadPoo	Manual testing	2A69913940794CAE	0.105

PRP results:

date

userid

compid

cofactors

res64

PRP

2020-01-30T01:54:26

Jinyuan Wang

Manual testing

303757575480788269129

35C7552E668AD014

2020-01-30T09:38:12

ANONYMOUS

dory

303757575480788269129

35C7552E668AD014

2020-02-01T22:55:47

Luigi Morelli

9800X

303757575480788269129

35C7552E668AD014

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 = 1939909, B2 = 30000000 (P-1 stage 2)

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

B1 = 1939909 (P-1 stage 1)

B1 = 1000000 (P-1 stage 1)

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁰

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

2⁵⁷

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

Last modified: 2022-03-24T12:31:06+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