M1930823 Mersenne number exponent details

Residue

Status

L-L

6F708EB03533E8CF

double-checked

PRP

-unknown-

-unknown-

	Trial Factoring	P-1 Factoring	Combined
Limit	GHz-days	Probability	B1	B2	GHz-days	Probability	GHz-days	Probability	Prob over default TF
Actual	2⁶⁸	30.8702	69.1176%	8000000	320000000	1.9665	9.7445%	32.8366	72.1270%	3.0093%
PrimeNet	2⁵⁸	0.0199	63.7931%	8000	140000	0.0012	2.4620%	0.0211	64.6845%	0.8914%
GPU72	2⁶²	0.3182	66.1290%	8000	90000	0.0010	1.1507%	0.3192	66.5188%	0.3897%
Difference	+6	+30.5520	+2.9886%	+7992000	+319910000	+1.9655	+8.5938%	+32.5175	+5.6082%	+5.6082%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁸

30.8702

69.1176%

8000000

320000000

1.9665

9.7445%

32.8366

72.1270%

3.0093%

PrimeNet

2⁵⁸

0.0199

63.7931%

8000

140000

0.0012

2.4620%

0.0211

64.6845%

0.8914%

GPU72

2⁶²

0.3182

66.1290%

8000

90000

0.0010

1.1507%

0.3192

66.5188%

0.3897%

Difference

+30.5520

+2.9886%

+7992000

+319910000

+1.9655

+8.5938%

+32.5175

+5.6082%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1930823	12389404182583206224687	23	73.392	3208322094408241 41 × 78251758400201	2020-01-20	41	78251758400201	1,660.0	335,367	626,373

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

1930823

12389404182583206224687

73.392

3208322094408241
41 × 78251758400201

2020-01-20

78251758400201

1,660.0

335,367

626,373

	GHz-Days	worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved
2011-09-06T02:49:00	kurly	hex	1000000	30000000		-		-	-	0.203	-	-	5.689%
2018-01-18T21:26:34	Jocelyn Larouche	low 4M	1930823	30000000	12	-		-	-	0.272	-	-	6.038%
2018-01-28T11:00:46	mikr	S061	8000000	320000000	12	-		-	-	1.966	-	-	9.744%

GHz-Days

worth

Factor
probability

date

userid

compid

stage

factor

digits

bits*

spent

saved

2011-09-06T02:49:00

kurly

hex

1000000

30000000

0.203

-

-

5.689%

2018-01-18T21:26:34

Jocelyn Larouche

low 4M

1930823

30000000

0.272

-

-

6.038%

2018-01-28T11:00:46

mikr

S061

8000000

320000000

1.966

-

-

9.744%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1998-12-21T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.020	-	-
2016-02-23T16:28:58	Mark Rose	Manual testing	2⁵⁸	2⁶⁰		-	-	0.060	-	-
2010-02-06T19:45:00	S485122	USB-W	2⁶⁰	2⁶¹		-	-	0.080	-	-
2016-02-23T16:28:58	Mark Rose	Manual testing	2⁶¹	2⁶²		-	-	0.159	-	-
2011-08-27T22:21:00	GrunwalderGIMP	Manual testing	2¹	2⁶³		-	-	0.827	-	-
2016-02-23T16:28:58	Mark Rose	Manual testing	2⁶²	2⁶³		-	-	0.508	-	-
2015-05-18T08:20:00	omylist	Manual testing	2⁶³	2⁶⁴		-	-	1.017	-	-
2015-05-18T08:20:00	omylist	Manual testing	2⁶⁴	2⁶⁵		-	-	1.935	-	-
2015-09-04T17:59:00	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	3.870	-	-
2018-02-26T10:32:50	TJAOI	Manual testing	2⁶⁶	2⁶⁷		-	-	7.740	-	-
2019-05-09T12:32:10	chuenkit	Manual testing	2⁶⁷	2⁶⁸		-	-	15.48	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	19.928 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:	19.928 GHz-days
Estimated T-Level:	24.482

Digits	B1	Complete	FacMiss
20	11000	8.712	0.016%
25	50000	0.776	46.019%
30	250000	0.048	95.307%
35	1000000	0.002	99.779%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		72	5.004
50000	5000000	12389404182583206224687	1	0.069
50000	7500000		178	14.85

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2008-11-13T01:54:00	maxybo	CB418E216	50000	5000000						3	0.208
2009-08-09T08:49:00	Piepen	T41-2000	50000	5000000						3	0.208
2010-12-25T19:53:00	Lupo	yorick	50000	5000000						3	0.208
2012-11-16T06:50:00	Donna Noble	PH2x6	50000	5000000						3	0.208
2013-12-11T18:44:00	Sara	Sara	50000	5000000						3	0.208
2015-03-23T18:09:00	arnaud	CHAMOT22	50000	5000000						3	0.208
2015-10-08T10:20:03	Sara	Sara	50000	5000000						3	0.208
2016-03-11T13:15:40	Bruce	Desk6	50000	5000000						3	0.208
2016-06-24T18:56:55	StarionHost	Bluto	50000	5000000						3	0.208
2016-09-15T18:34:50	Bruce	Desk6	50000	5000000						3	0.208
2017-02-22T04:11:00	Bruce	Desk6	50000	5000000						3	0.208
2017-08-21T02:02:01	Bruce	Desk6	50000	5000000						3	0.208
2017-12-31T04:41:59	Clark B. Wierda	CF-27	50000	5000000						3	0.208
2018-05-05T06:44:21	Bruce	Desk6	50000	5000000						3	0.208
2019-04-07T02:42:18	Chang Chia-Tche	ex-ctcpc	50000	5000000						3	0.208
2019-12-01T23:25:44	Keysarecool	Boat_Anchor	50000	5000000						3	0.208
2019-12-05T21:37:51	Alvin Bunk	i7-Core	50000	5000000						3	0.208
2019-12-11T03:27:23	Nesowa	entropy_generator_2	50000	5000000						3	0.208
2019-12-14T15:07:24	Keysarecool	Boat_Anchor	50000	5000000						3	0.208
2019-12-20T08:59:13	Alvin Bunk	BADCAT	50000	5000000						3	0.208
2019-12-26T18:06:36	Brett Walker	brain	50000	5000000						3	0.208
2020-01-06T12:20:49	Corey	Computer	50000	5000000						3	0.208
2020-01-20T08:51:35	mnd9	kitchen	50000	5000000	12389404182583206224687	73.392	1	2	2057047435340320	1	0.069
2020-01-23T02:04:13	mnd9	25836b	50000	5000000						3	0.208
2020-01-25T20:22:27	mnd9	75204b	50000	5000000						3	0.208
2022-04-07T09:50:22	TJAOI	Manual testing	50000	7500000						178	14.85

date	userid	compid	res64	spent (GHz-days)
1999-01-10T00:00:00	ANONYMOUS	v4_computers	6F708EB03533E8CF	0.105
2015-07-14T15:04:00	MadPoo	Manual testing	6F708EB03533E8CF	0.105

date

userid

compid

res64

spent (GHz-days)

1999-01-10T00:00:00

ANONYMOUS

v4_computers

6F708EB03533E8CF

0.105

2015-07-14T15:04:00

MadPoo

Manual testing

6F708EB03533E8CF

0.105

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 = 1930823, B2 = 30000000 (P-1 stage 2)

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

B1 = 1930823 (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

10¹³

10¹⁴

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