M1991153 Mersenne number exponent details

Residue

Status

L-L

E5D9138784810829

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	14.9230	68.6567%	1000000	30000000	0.2460	6.2504%	15.1689	70.6158%	1.9591%
PrimeNet	2⁵⁸	0.0193	63.7931%	8000	140000	0.0014	2.4767%	0.0207	64.6898%	0.8967%
GPU72	2⁶²	0.3085	66.1290%	8000	110000	0.0013	1.2355%	0.3098	66.5475%	0.4185%
Difference	+5	+14.6144	+2.5277%	+992000	+29890000	+0.2447	+5.0149%	+14.8591	+4.0683%	+4.0683%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

14.9230

68.6567%

1000000

30000000

0.2460

6.2504%

15.1689

70.6158%

1.9591%

PrimeNet

2⁵⁸

0.0193

63.7931%

8000

140000

0.0014

2.4767%

0.0207

64.6898%

0.8967%

GPU72

2⁶²

0.3085

66.1290%

8000

110000

0.0013

1.2355%

0.3098

66.5475%

0.4185%

Difference

+14.6144

+2.5277%

+992000

+29890000

+0.2447

+5.0149%

+14.8591

+4.0683%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1991153	1213970110051695233157751	25	80.006	304840991639440875 3 × 5³ × 812909311038509	2017-06-15	125	812909311038509	196,844	4,222,454	7,886,369

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

1991153

1213970110051695233157751

80.006

304840991639440875
3 × 5³ × 812909311038509

2017-06-15

125

812909311038509

196,844

4,222,454

7,886,369

	GHz-Days	worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved
2011-02-21T20:41:00	kurly	kurlytop	1000000	30000000		-		-	-	0.246	-	-	6.250%

GHz-Days

worth

Factor
probability

date

userid

compid

stage

factor

digits

bits*

spent

saved

2011-02-21T20:41:00

kurly

kurlytop

1000000

30000000

0.246

-

-

6.250%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1998-12-27T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.019	-	-
2016-02-23T16:29:02	Mark Rose	Manual testing	2⁵⁸	2⁶⁰		-	-	0.058	-	-
2009-12-11T12:47:00	S485122	USB-W	2⁶⁰	2⁶¹		-	-	0.077	-	-
2016-02-23T16:29:02	Mark Rose	Manual testing	2⁶¹	2⁶²		-	-	0.154	-	-
2011-07-01T19:07:00	GrunwalderGIMP	Manual testing	2¹	2⁶³		-	-	0.802	-	-
2016-02-23T16:29:02	Mark Rose	Manual testing	2⁶²	2⁶³		-	-	0.493	-	-
2015-03-06T09:37:00	lycorn	Manual testing	2⁶³	2⁶⁴		-	-	0.986	-	-
2015-03-06T09:37:00	lycorn	Manual testing	2⁶⁴	2⁶⁵		-	-	1.876	-	-
2015-09-12T12:52:00	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	3.753	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	3.241 GHz-days
Estimated T-Level:	1.900

Digits	B1	Curves	Complete	FacMiss
20	11000	38 / 100	0.380	68.255%
25	50000	38 / 280	0.136	87.288%

New Calculation Method

Total ECM effort:	3.241 GHz-days
Estimated T-Level:	1.900

Digits	B1	Complete	FacMiss
20	11000	1.233	29.132%
25	50000	0.111	89.502%
30	250000	0.007	99.319%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		30	2.536
50000	5000000	1213970110051695233157751	1	0.085
50000	5600000		7	0.620

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2008-11-25T10:20:00	oodaira	Win02	50000	5000000						3	0.254
2009-08-31T18:22:00	SubPrime	abd0	50000	5000000						3	0.254
2011-02-01T21:59:00	Lupo	yorick	50000	5000000						3	0.254
2012-12-17T00:23:00	OS1	L3	50000	5000000						3	0.254
2014-02-23T10:49:00	OS1	L3	50000	5000000						3	0.254
2015-06-26T03:07:00	dragon325	Falken-i7-920	50000	5000000						3	0.254
2016-02-15T02:20:57	Sintax	cloud2	50000	5000000						3	0.254
2016-06-04T04:43:19	Bruce	Desk6	50000	5000000						3	0.254
2016-07-11T00:21:33	Bruce	test	50000	5000000						3	0.254
2016-11-15T16:02:28	Bruce	Desk6	50000	5000000						3	0.254
2017-06-15T07:13:43	Bruce	Desk6	50000	5000000	1213970110051695233157751	80.006	1	2		1	0.085
2022-03-26T22:01:32	Alex Kruppa	lily	50000	5600000						7	0.620

date	userid	compid	res64	spent (GHz-days)
1999-01-17T00:00:00	ANONYMOUS	v4_computers	E5D9138784810829	0.131
2015-07-03T04:32:00	MadPoo	Manual testing	E5D9138784810829	0.131

date

userid

compid

res64

spent (GHz-days)

1999-01-17T00:00:00

ANONYMOUS

v4_computers

E5D9138784810829

0.131

2015-07-03T04:32:00

MadPoo

Manual testing

E5D9138784810829

0.131

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)

10¹

10²

10³

10⁴

10⁵

10⁶

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

10¹²

10¹³

10¹⁴

10¹⁵

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