M1034849 Mersenne number exponent details

Residue

Status

L-L

E8192230F6D1FCD6

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	28.7133	70.1493%	10000000	1110000000	3.0054	11.7914%	31.7187	73.6691%	3.5198%
PrimeNet	2⁵⁶	0.0093	64.2857%	4500	60000	0.0003	1.9529%	0.0096	64.9832%	0.6975%
GPU72	2⁶⁰	0.1484	66.6667%	4500	18000	0.0002	0.6155%	0.1486	66.8718%	0.2052%
Difference	+7	+28.5649	+3.4826%	+9995500	+1109982000	+3.0052	+11.1759%	+31.5700	+6.7973%	+6.7973%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

28.7133

70.1493%

10000000

1110000000

3.0054

11.7914%

31.7187

73.6691%

3.5198%

PrimeNet

2⁵⁶

0.0093

64.2857%

4500

60000

0.0003

1.9529%

0.0096

64.9832%

0.6975%

GPU72

2⁶⁰

0.1484

66.6667%

4500

18000

0.0002

0.6155%

0.1486

66.8718%

0.2052%

Difference

+28.5649

+3.4826%

+9995500

+1109982000

+3.0052

+11.1759%

+31.5700

+6.7973%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1034849	7997663577475670753	19	62.794	3864169351024 2⁴ × 17 × 23 × 617674129	2009-10-24	23	617674129	1.0010	1.4463	2.7012

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

1034849

7997663577475670753

62.794

3864169351024
2⁴ × 17 × 23 × 617674129

2009-10-24

617674129

1.0010

1.4463

2.7012

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2002-01-22T00:00:00	Jocelyn Larouche	v4_computers	1000	10000		-		-	-	6.40496e-5	-	-	0.036%
2002-01-28T00:00:00	Jocelyn Larouche	v4_computers	1000	10000		-		-	-	6.40496e-5	-	-	0.036%
2002-05-11T00:00:00	Jocelyn Larouche	v4_computers	5000	5000		-		-	-	0.000	-	-	0.063%
2016-03-17T18:59:25	alpertron	Manual testing	300000	10000000	12	-		-	-	0.036	-	-	4.082%
2021-07-17T20:28:35	ViliamF	3	10000000	1110000000		-	skipped known factor: 7997663577475670753	-	-	3.005	-	-	11.791%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2001-11-10T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁷		-	-	0.019	-	-
2003-02-02T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.037	-	-
2022-03-07T17:30:27	LordJulius	Manual testing	2⁵⁸	2⁶⁰		-	-	0.111	-	-
2009-02-26T18:53:00	Sturle Sunde	danzi.ifi	2⁶⁰	2⁶¹		-	-	0.148	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	17.458 GHz-days
Estimated T-Level:	25.344

Digits	B1	Curves	Complete	FacMiss
20	11000	324 / 100	3.240	3.853%
25	50000	324 / 280	1.157	31.373%
30	250000	44 / 640	0.069	93.351%

New Calculation Method

Total ECM effort:	17.458 GHz-days
Estimated T-Level:	25.344

Digits	B1	Complete	FacMiss
20	11000	14.769	0.000%
25	50000	1.616	19.866%
30	250000	0.131	87.697%
35	1000000	0.009	99.130%

ECM Summary

B1	B2	factor	curves	GHz-days
		7997663577475670753	1	0.00000e+0
50000	5000000		280	9.78
250000	25000000		44	7.681

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2007-09-22T07:43:00	Chad Davis	Bayes	50000	5000000						1	0.035
2008-02-20T12:18:00	Sturle Sunde	minister	50000	5000000						3	0.105
2008-11-29T21:57:00	Sturle Sunde	v21	50000	5000000						3	0.105
2009-03-22T16:44:00	linded	kctz73a	50000	5000000						3	0.105
2009-08-03T13:11:00	JimBa	FWserv	50000	5000000						3	0.105
2009-10-24T09:52:00	JimBa	HPserv			7997663577475670753	62.794		1		1	-
2017-03-17T17:36:42	TJAOI	Manual testing	50000	5000000						86	3.003
2017-07-21T13:30:25	TJAOI	Manual testing	50000	5000000						90	3.142
2018-03-02T13:49:43	TJAOI	Manual testing	50000	5000000						91	3.177
2020-06-29T11:34:40	TJAOI	Manual testing	250000	25000000						44	7.681

date	userid	compid	res64	spent (GHz-days)
2002-02-10T00:00:00	ANONYMOUS	v4_computers	E8192230F6D1FCD6	0.031

date

userid

compid

res64

spent (GHz-days)

2002-02-10T00:00:00

ANONYMOUS

v4_computers

E8192230F6D1FCD6

0.031

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-28T18:54:33

Oliver Kruse

GTX-1

7997663577475670753

55985259DFC769__

2017-10-15T20:23:35

Oliver Kruse

Threadripper

7997663577475670753

55985259DFC769__

2017-12-28T05:52:37

ATH

ec2-1xf

7997663577475670753

55985259DFC769__

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 = 10000000, B2 = 1110000000 (P-1 stage 2)

B1 = 10000000 (P-1 stage 1)

B1 = 300000, B2 = 10000000 (P-1 stage 2)

B1 = 300000 (P-1 stage 1)

B1 = 5000 (P-1 stage 1)

B1 = 1000, B2 = 10000 (P-1 stage 2)

B1 = 1000 (P-1 stage 1)

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

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