M1909987 Mersenne number exponent details

Residue

Status

L-L

946072B6F7567D0C

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	31.2070	69.1176%	8000000	320000000	1.9665	9.7352%	33.1734	72.1241%	3.0065%
PrimeNet	2⁵⁷	0.0101	63.1579%	9000	160000	0.0014	3.0410%	0.0114	64.2782%	1.1204%
GPU72	2⁶¹	0.1608	65.5738%	10000	170000	0.0015	1.7597%	0.1623	66.1796%	0.6058%
Difference	+7	+31.0461	+3.5439%	+7990000	+319830000	+1.9650	+7.9755%	+33.0111	+5.9445%	+5.9445%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁸

31.2070

69.1176%

8000000

320000000

1.9665

9.7352%

33.1734

72.1241%

3.0065%

PrimeNet

2⁵⁷

0.0101

63.1579%

9000

160000

0.0014

3.0410%

0.0114

64.2782%

1.1204%

GPU72

2⁶¹

0.1608

65.5738%

10000

170000

0.0015

1.7597%

0.1623

66.1796%

0.6058%

Difference

+31.0461

+3.5439%

+7990000

+319830000

+1.9650

+7.9755%

+33.0111

+5.9445%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1909987	12940575883523516636593	23	73.454	3387608366843208 2³ × 3 × 163 × 865953059009	2019-12-14	163	865953059009	1,779.4	3,711.3	6,931.6

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

1909987

12940575883523516636593

73.454

3387608366843208
2³ × 3 × 163 × 865953059009

2019-12-14

163

865953059009

1,779.4

3,711.3

6,931.6

	GHz-Days	worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved
2011-06-14T21:58:00	kurly	kurlytop	1000000	30000000		-		-	-	0.203	-	-	5.682%
2017-12-08T09:28:23	mikr	S066	8000000	320000000	12	-		-	-	1.966	-	-	9.735%

GHz-Days

worth

Factor
probability

date

userid

compid

stage

factor

digits

bits*

spent

saved

2011-06-14T21:58:00

kurly

kurlytop

1000000

30000000

0.203

-

-

5.682%

2017-12-08T09:28:23

mikr

S066

8000000

320000000

1.966

-

-

9.735%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2011-04-14T00:00:00	GrunwalderGIMP	v4_computers	2¹	2⁵⁶		-	-	0.005	-	-
2011-04-14T00:00:00	GrunwalderGIMP	v4_computers	2⁵⁶	2⁵⁷		-	-	0.005	-	-
2003-01-09T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.020	-	-
2011-04-14T00:00:00	GrunwalderGIMP	v4_computers	2⁵⁷	2⁵⁸		-	-	0.010	-	-
2011-04-14T00:00:00	GrunwalderGIMP	v4_computers	2⁵⁸	2⁵⁹		-	-	0.020	-	-
2011-04-14T00:00:00	GrunwalderGIMP	v4_computers	2⁵⁹	2⁶⁰		-	-	0.040	-	-
2011-04-14T00:00:00	GrunwalderGIMP	v4_computers	2⁶⁰	2⁶¹		-	-	0.080	-	-
2009-05-27T16:44:00	Architects Cubed	i4l_1	2⁶⁰	2⁶¹		-	-	0.080	-	-
2011-03-09T08:06:00	GrunwalderGIMP	GWPrime02	2⁶¹	2⁶²		-	-	0.161	-	-
2011-03-09T11:34:00	GrunwalderGIMP	GWPrime02	2⁶²	2⁶³		-	-	0.514	-	-
2015-05-18T08:20:00	omylist	Manual testing	2⁶³	2⁶⁴		-	-	1.028	-	-
2015-05-19T20:57:00	monst	Manual testing	2⁶⁴	2⁶⁵		-	-	1.956	-	-
2015-09-01T08:49:00	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	3.912	-	-
2017-03-15T08:26:28	Smok_bmv	Manual testing	2⁶⁶	2⁶⁷		-	-	7.825	-	-
2019-04-27T00:32:11	chuenkit	Manual testing	2⁶⁷	2⁶⁸		-	-	15.65	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	19.140 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:	19.140 GHz-days
Estimated T-Level:	24.482

Digits	B1	Complete	FacMiss
20	11000	8.526	0.020%
25	50000	0.772	46.199%
30	250000	0.048	95.337%
35	1000000	0.002	99.781%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		57	3.956
50000	5000000	12940575883523516636593	1	0.069
50000	6600000		193	15.11

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2008-11-06T15:50:00	David Campeau		50000	5000000						3	0.208
2009-08-02T08:09:00	James Hintz	03_071509	50000	5000000						3	0.208
2010-11-30T10:31:00	James Hintz	ryan	50000	5000000						3	0.208
2012-10-20T13:18:00	Donna Noble	i3-2100t	50000	5000000						3	0.208
2013-11-22T22:09:00	arnaud	srv-630	50000	5000000						3	0.208
2014-10-08T10:38:00	Sara	Sara	50000	5000000						3	0.208
2015-08-12T10:08:00	Sara	Sara	50000	5000000						3	0.208
2016-01-29T14:34:16	Sara	Sara	50000	5000000						3	0.208
2016-06-15T08:05:20	Bruce	Desk6	50000	5000000						3	0.208
2016-08-21T17:39:58	Bruce	test	50000	5000000						3	0.208
2017-02-04T22:36:11	Bruce	Desk6	50000	5000000						3	0.208
2017-07-24T21:49:25	Bruce	Desk6	50000	5000000						3	0.208
2017-12-10T14:46:56	Lelikoid	QH	50000	5000000						3	0.208
2018-04-08T17:21:48	Bruce	Desk6	50000	5000000						3	0.208
2018-09-14T23:50:48	Bruce	Desk6	50000	5000000						3	0.208
2019-11-27T22:18:23	Keysarecool	Boat_Anchor	50000	5000000						3	0.208
2019-12-02T18:55:16	nranks	wlaptop	50000	5000000						3	0.208
2019-12-06T04:02:46	Nesowa	entropy_generator_2	50000	5000000						3	0.208
2019-12-09T20:19:20	daveward2005	Davy	50000	5000000						3	0.208
2019-12-14T05:17:54	Keysarecool	Boat_Anchor	50000	5000000	12940575883523516636593	73.454	1	2	5427901471320391	1	0.069
2022-01-06T11:57:10	TJAOI	Manual testing	50000	6600000						193	15.11

date	userid	compid	res64	spent (GHz-days)
1997-12-09T00:00:00	ANONYMOUS	v4_computers	946072B6F7567D0C	0.104
1999-01-10T00:00:00	ANONYMOUS	v4_computers	946072B6F7567D0C	0.104
2015-07-04T19:28:00	MadPoo	Manual testing	946072B6F7567D0C	0.104

date

userid

compid

res64

spent (GHz-days)

1997-12-09T00:00:00

ANONYMOUS

v4_computers

946072B6F7567D0C

0.104

1999-01-10T00:00:00

ANONYMOUS

v4_computers

946072B6F7567D0C

0.104

2015-07-04T19:28:00

MadPoo

Manual testing

946072B6F7567D0C

0.104

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)

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

10¹²

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