M2056193 Mersenne number exponent details

Residue

Status

L-L

E8EA4A802F7829F9

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	14.4509	68.6567%	270000	4860000	0.0496	3.7936%	14.5005	69.8457%	1.1890%
PrimeNet	2⁵⁸	0.0187	63.7931%	9000	160000	0.0016	2.6671%	0.0203	64.7588%	0.9657%
GPU72	2⁶²	0.2988	66.1290%	9000	120000	0.0014	1.3311%	0.3002	66.5799%	0.4509%
Difference	+5	+14.1522	+2.5277%	+261000	+4740000	+0.0481	+2.4624%	+14.2003	+3.2658%	+3.2658%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

14.4509

68.6567%

270000

4860000

0.0496

3.7936%

14.5005

69.8457%

1.1890%

PrimeNet

2⁵⁸

0.0187

63.7931%

9000

160000

0.0016

2.6671%

0.0203

64.7588%

0.9657%

GPU72

2⁶²

0.2988

66.1290%

9000

120000

0.0014

1.3311%

0.3002

66.5799%

0.4509%

Difference

+14.1522

+2.5277%

+261000

+4740000

+0.0481

+2.4624%

+14.2003

+3.2658%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2056193	3175754263306914039712094951	28	91.359	772241288465361481075 5² × 31 × 996440372213369653	2016-07-17	31	996440372213369653	414,667,582	5.176e+9	9.667e+9

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

2056193

3175754263306914039712094951

91.359

772241288465361481075
5² × 31 × 996440372213369653

2016-07-17

996440372213369653

414,667,582

5.176e+9

9.667e+9

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2003-02-24T00:00:00	ANONYMOUS	v4_computers	2048	204800		-		-	-	0.001	-	-	0.275%
2009-06-21T15:12:00	harlee	T7500_2200	20000	260000		-		-	-	0.003	-	-	1.016%
2010-12-26T02:29:00	Jocelyn Larouche	Manual testing	30000	30000		-		-	-	0.003	-	-	0.413%
2011-01-06T01:06:00	Jocelyn Larouche	Manual testing	50000	50000		-		-	-	0.005	-	-	0.593%
2011-01-22T00:55:00	James Heinrich	i7-920	135000	2902500		-		-	-	0.027	-	-	3.045%
2014-10-26T00:59:00	Jocelyn Larouche	Manual testing	166215	166215		-		-	-	0.016	-	-	1.209%
2016-05-15T21:00:27	Jocelyn Larouche	Manual testing	270000	4860000	6	-		-	-	0.050	-	-	3.794%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2016-02-23T16:29:04	Mark Rose	Manual testing	2¹	2⁶⁰		-	-	0.075	-	-
2009-01-03T05:19:00	Sturle Sunde	gorky.ifi	2⁶⁰	2⁶¹		-	-	0.075	-	-
2012-03-11T19:47:00	Sebastian Hornbostel	Manual testing	2⁶¹	2⁶²		-	-	0.149	-	-
2013-09-01T20:20:00	ramgeis	Manual testing	2⁶²	2⁶³		-	-	0.477	-	-
2015-04-21T09:19:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.955	-	-
2015-04-21T09:19:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.817	-	-
2015-11-03T10:10:05	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	3.634	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	2.805 GHz-days
Estimated T-Level:	1.600

Digits	B1	Curves	Complete	FacMiss
20	11000	32 / 100	0.320	72.498%
25	50000	32 / 280	0.114	89.182%

New Calculation Method

Total ECM effort:	2.805 GHz-days
Estimated T-Level:	1.600

Digits	B1	Complete	FacMiss
20	11000	1.056	34.769%
25	50000	0.095	90.934%
30	250000	0.006	99.415%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		24	2.037
50000	5000000	3175754263306914039712094951	1	0.085
50000	6837944		7	0.683

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-02-27T16:19:00	maxybo	CB418E216	50000	5000000						3	0.255
2009-10-24T13:25:00	ANONYMOUS	fn-asterisk	50000	5000000						3	0.255
2011-04-16T02:51:00	James Hintz	ryan	50000	5000000						3	0.255
2013-03-08T13:28:00	Donna Noble	opt4820	50000	5000000						3	0.255
2014-04-14T14:14:00	OS1	L3	50000	5000000						3	0.255
2015-07-13T12:04:00	guru	w1	50000	5000000						3	0.255
2016-02-19T23:24:12	Sintax	cloud	50000	5000000						3	0.255
2016-05-06T11:25:47	Bruce	Desk6	50000	5000000						3	0.255
2016-07-17T23:33:57	Bruce	test	50000	5000000	3175754263306914039712094951	91.359	1	2		1	0.085
2022-05-22T10:39:58	debrouxl	dl380g9-1	50000	6837944						7	0.683

date	userid	compid	res64	spent (GHz-days)
1999-01-29T00:00:00	ANONYMOUS	v4_computers	E8EA4A802F7829F9	0.135
2016-07-16T00:40:38	Mark Rose	raphael	E8EA4A802F7829F9	0.135

date

userid

compid

res64

spent (GHz-days)

1999-01-29T00:00:00

ANONYMOUS

v4_computers

E8EA4A802F7829F9

0.135

2016-07-16T00:40:38

Mark Rose

raphael

E8EA4A802F7829F9

0.135

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 = 270000, B2 = 4860000 (P-1 stage 2)

B1 = 135000, B2 = 2902500 (P-1 stage 2)

B1 = 270000 (P-1 stage 1)

B1 = 166215 (P-1 stage 1)

B1 = 135000 (P-1 stage 1)

B1 = 50000 (P-1 stage 1)

B1 = 20000, B2 = 260000 (P-1 stage 2)

B1 = 30000 (P-1 stage 1)

B1 = 20000 (P-1 stage 1)

B1 = 2048, B2 = 204800 (P-1 stage 2)

B1 = 2048 (P-1 stage 1)

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

10¹²

10¹³

10¹⁴

10¹⁵

10¹⁶

10¹⁷

10¹⁸

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