M1004449 Mersenne number exponent details

Residue

Status

L-L

6846746D0C97A16B

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	29.5823	70.1493%	10000000	1110000000	3.0054	11.7630%	32.5877	73.6606%	3.5114%
PrimeNet	2⁵⁶	0.0096	64.2857%	4500	60000	0.0003	1.9405%	0.0099	64.9788%	0.6930%
GPU72	2⁶⁰	0.1529	66.6667%	4500	16000	0.0002	0.5776%	0.1531	66.8592%	0.1925%
Difference	+7	+29.4294	+3.4826%	+9995500	+1109984000	+3.0052	+11.1854%	+32.4346	+6.8014%	+6.8014%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

29.5823

70.1493%

10000000

1110000000

3.0054

11.7630%

32.5877

73.6606%

3.5114%

PrimeNet

2⁵⁶

0.0096

64.2857%

4500

60000

0.0003

1.9405%

0.0099

64.9788%

0.6930%

GPU72

2⁶⁰

0.1529

66.6667%

4500

16000

0.0002

0.5776%

0.1531

66.8592%

0.1925%

Difference

+29.4294

+3.4826%

+9995500

+1109984000

+3.0052

+11.1854%

+32.4346

+6.8014%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1004449	6345149350738803559	19	62.460	3158522409171 3 × 41 × 2683 × 9571019	2007-09-17	2683	9571019	0.7367	0.0225	0.0419

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

1004449

6345149350738803559

62.460

3158522409171
3 × 41 × 2683 × 9571019

2007-09-17

2683

9571019

0.7367

0.0225

0.0419

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2000-12-14T00:00:00	ANONYMOUS	v4_computers	50000	1000000		-		-	-	0.004	-	-	1.703%
2003-11-16T00:00:00	ANONYMOUS	v4_computers	2048	204800		-		-	-	0.001	-	-	0.224%
2006-01-15T00:00:00	Jocelyn Larouche	v4_computers	60000	60000		-		-	-	0.003	-	-	0.580%
2016-03-17T18:58:57	alpertron	Manual testing	300000	10000000	12	-	skipped known factor: 6345149350738803559	-	-	0.036	-	-	4.067%
2021-06-21T11:22:46	ViliamF	3	10000000	1110000000		-	skipped known factor: 6345149350738803559	-	-	3.005	-	-	11.763%

ECM factoring results:

Old Calculation Method

Total ECM effort:	17.426 GHz-days
Estimated T-Level:	25.344

Digits	B1	Curves	Complete	FacMiss
20	11000	325 / 100	3.250	3.815%
25	50000	325 / 280	1.161	31.261%
30	250000	44 / 640	0.069	93.351%

New Calculation Method

Total ECM effort:	17.426 GHz-days
Estimated T-Level:	25.344

Digits	B1	Complete	FacMiss
20	11000	14.808	0.000%
25	50000	1.620	19.795%
30	250000	0.132	87.678%
35	1000000	0.009	99.129%

ECM Summary

B1	B2	factor	curves	GHz-days
		6345149350738803559	1	0.00000e+0
50000	5000000		281	9.77
250000	25000000		44	7.652

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2007-09-17T22:44:00	Chad Davis	Bayes			6345149350738803559	62.460		1		1	-
2017-01-27T18:39:41	TJAOI	Manual testing	50000	5000000						100	3.478
2017-02-17T21:10:45	TJAOI	Manual testing	50000	5000000						90	3.130
2018-02-02T17:07:36	TJAOI	Manual testing	50000	5000000						91	3.165
2020-03-16T11:26:52	TJAOI	Manual testing	250000	25000000						44	7.652

date	userid	compid	res64	spent (GHz-days)
2001-01-21T00:00:00	ANONYMOUS	v4_computers	6846746D0C97A16B	0.030

date

userid

compid

res64

spent (GHz-days)

2001-01-21T00:00:00

ANONYMOUS

v4_computers

6846746D0C97A16B

0.030

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-28T16:11:58

Oliver Kruse

GTX-1

6345149350738803559

A745B583E407C3__

2017-10-15T14:33:38

Oliver Kruse

Threadripper

6345149350738803559

A745B583E407C3__

2017-12-25T10:48:47

ATH

ec2-1xf

6345149350738803559

A745B583E407C3__

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 = 50000, B2 = 1000000 (P-1 stage 2)

B1 = 60000 (P-1 stage 1)

B1 = 50000 (P-1 stage 1)

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

B1 = 2048 (P-1 stage 1)

10²

10³

10⁴

10⁵

10⁶

10⁷

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