M1905689 Mersenne number exponent details

Residue

Status

L-L

6B8D7AFFCA31288B

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	2⁶⁷	15.5922	68.6567%	1000000	30000000	0.2029	6.2199%	15.7952	70.6062%	1.9495%
PrimeNet	2⁵⁷	0.0101	63.1579%	9000	160000	0.0014	3.0397%	0.0114	64.2778%	1.1199%
GPU72	2⁶¹	0.1612	65.5738%	10000	160000	0.0014	1.7284%	0.1626	66.1688%	0.5950%
Difference	+6	+15.4310	+3.0829%	+990000	+29840000	+0.2015	+4.4915%	+15.6325	+4.4374%	+4.4374%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

15.5922

68.6567%

1000000

30000000

0.2029

6.2199%

15.7952

70.6062%

1.9495%

PrimeNet

2⁵⁷

0.0101

63.1579%

9000

160000

0.0014

3.0397%

0.0114

64.2778%

1.1199%

GPU72

2⁶¹

0.1612

65.5738%

10000

160000

0.0014

1.7284%

0.1626

66.1688%

0.5950%

Difference

+15.4310

+3.0829%

+990000

+29840000

+0.2015

+4.4915%

+15.6325

+4.4374%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1905689	83383390023197002423490383	26	86.108	21877491559010153919 3 × 151883 × 48013913251231	2017-07-19	151883	48013913251231	9,467,728	205,776	384,332

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

1905689

83383390023197002423490383

86.108

21877491559010153919
3 × 151883 × 48013913251231

2017-07-19

151883

48013913251231

9,467,728

205,776

384,332

	GHz-Days	worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved
2011-06-01T14:08:00	kurly	slice	1000000	30000000		-		-	-	0.203	-	-	6.220%

GHz-Days

worth

Factor
probability

date

userid

compid

stage

factor

digits

bits*

spent

saved

2011-06-01T14:08:00

kurly

slice

1000000

30000000

0.203

-

-

6.220%

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	-	-
2002-01-02T00:00:00	Jocelyn Larouche	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		-	-	0.081	-	-
2009-05-25T16:29:00	Architects Cubed	i4l_1	2⁶⁰	2⁶¹		-	-	0.081	-	-
2011-02-08T18:08:00	GrunwalderGIMP	GWPrime02	2⁶¹	2⁶²		-	-	0.161	-	-
2011-02-08T21:56:00	GrunwalderGIMP	GWPrime02	2⁶²	2⁶³		-	-	0.515	-	-
2015-05-17T05:14:00	omylist	Manual testing	2⁶³	2⁶⁴		-	-	1.030	-	-
2015-05-19T06:11:00	omylist	Manual testing	2⁶⁴	2⁶⁵		-	-	1.961	-	-
2015-08-31T08:30:00	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	3.921	-	-
2017-03-15T08:26:27	Smok_bmv	Manual testing	2⁶⁶	2⁶⁷		-	-	7.843	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	21.681 GHz-days
Estimated T-Level:	24.607

Digits	B1	Curves	Complete	FacMiss
20	11000	258 / 100	2.580	7.480%
25	50000	258 / 280	0.921	39.729%

New Calculation Method

Total ECM effort:	21.681 GHz-days
Estimated T-Level:	24.607

Digits	B1	Complete	FacMiss
20	11000	9.075	0.011%
25	50000	0.848	42.816%
30	250000	0.055	94.623%
35	1000000	0.003	99.724%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		33	2.290
50000	5000000	83383390023197002423490383	3	0.208
50000	6600000		215	16.83
200000	30496558		7	2.352

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-05-07T15:14:00	Luigi Morelli	AMD64x2	50000	5000000						3	0.208
2009-07-29T00:26:00	James Hintz	16_071509	50000	5000000						3	0.208
2010-11-25T21:49:00	Martti Järvi	slave	50000	5000000						3	0.208
2012-10-18T06:58:00	Donna Noble	CCI_PH2_955	50000	5000000						3	0.208
2014-03-15T02:06:00	Andy Incline	Office-PC	50000	5000000						3	0.208
2014-08-23T17:53:00	Sara	Sara	50000	5000000						3	0.208
2015-07-18T18:08:00	Sara	Sara	50000	5000000						3	0.208
2016-01-07T09:54:58	Sara	Sara	50000	5000000						3	0.208
2016-06-12T22:26:22	Bruce	Desk6	50000	5000000						3	0.208
2016-08-19T03:06:05	Bruce	test	50000	5000000						3	0.208
2017-02-03T19:09:40	Bruce	Desk6	50000	5000000						3	0.208
2017-07-19T06:01:19	Bruce	Desk6	50000	5000000	83383390023197002423490383	86.108	3	2		3	0.208
2021-10-24T10:41:08	George Woltman	x64-debug	200000	30496558						7	2.352
2022-01-18T14:07:36	TJAOI	Manual testing	50000	6600000						215	16.83

date	userid	compid	res64	spent (GHz-days)
2015-07-14T15:04:00	MadPoo	Manual testing	6B8D7AFFCA31288B	0.103

date

userid

compid

res64

spent (GHz-days)

2015-07-14T15:04:00

MadPoo

Manual testing

6B8D7AFFCA31288B

0.103

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

B1 = 1000000 (P-1 stage 1)

10⁴

10⁵

10⁶

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