M1569317 Mersenne number exponent details

Residue

Status

L-L

7321837571C67678

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	18.9343	68.6567%	10000000	200000000	1.3181	9.7344%	20.2524	71.7078%	3.0511%
PrimeNet	2⁵⁷	0.0122	63.1579%	7000	110000	0.0008	2.4773%	0.0131	64.0706%	0.9127%
GPU72	2⁶¹	0.1957	65.5738%	6500	60000	0.0006	1.0518%	0.1964	65.9359%	0.3621%
Difference	+6	+18.7386	+3.0829%	+9993500	+199940000	+1.3175	+8.6826%	+20.0561	+5.7719%	+5.7719%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

18.9343

68.6567%

10000000

200000000

1.3181

9.7344%

20.2524

71.7078%

3.0511%

PrimeNet

2⁵⁷

0.0122

63.1579%

7000

110000

0.0008

2.4773%

0.0131

64.0706%

0.9127%

GPU72

2⁶¹

0.1957

65.5738%

6500

60000

0.0006

1.0518%

0.1964

65.9359%

0.3621%

Difference

+18.7386

+3.0829%

+9993500

+199940000

+1.3175

+8.6826%

+20.0561

+5.7719%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1569317	41711097608582628662729	23	75.143	13289570433692692 2² × 6653027 × 499380599	2015-12-13	6653027	499380599	5,754.1	2.1696	3.2912

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

1569317

41711097608582628662729

75.143

13289570433692692
2² × 6653027 × 499380599

2015-12-13

6653027

499380599

5,754.1

2.1696

3.2912

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2003-09-29T00:00:00	Team Prime Rib	v4_computers	20000	300000		-		-	-	0.002	-	-	1.006%
2011-01-30T14:15:00	James Heinrich	WHS	80000	1380000		-		-	-	0.010	-	-	2.218%
2013-11-24T11:45:00	David Campeau	i5-2500k	950000	27550000		-		-	-	0.155	-	-	5.965%
2015-04-05T09:11:00	VictordeHollander	Manual testing	10000000	200000000		-		-	-	1.318	-	-	9.734%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1998-10-25T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁷		-	-	0.012	-	-
2003-08-08T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.024	-	-
2010-05-03T03:31:00	Architects Cubed	a3_bu2	2⁶⁰	2⁶¹		-	-	0.098	-	-
2010-05-24T21:18:00	GrunwalderGIMP	Manual testing	2¹	2⁶³		-	-	1.017	-	-
2015-02-24T22:59:00	snme2pm1	Manual testing	2⁶³	2⁶⁴		-	-	1.251	-	-
2015-02-24T22:59:00	snme2pm1	Manual testing	2⁶⁴	2⁶⁵		-	-	2.381	-	-
2015-10-11T16:52:25	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	4.762	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	14.046 GHz-days
Estimated T-Level:	24.482

Digits	B1	Curves	Complete	FacMiss
20	11000	251 / 100	2.510	8.025%
25	50000	251 / 280	0.896	40.737%

New Calculation Method

Total ECM effort:	14.046 GHz-days
Estimated T-Level:	24.482

Digits	B1	Complete	FacMiss
20	11000	8.097	0.030%
25	50000	0.732	48.105%
30	250000	0.045	95.594%
35	1000000	0.002	99.794%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		249	13.93
50000	5000000	41711097608582628662729	2	0.112

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2008-03-10T16:59:00	Scott Kurowski	UW4	50000	5000000						3	0.168
2009-04-30T08:13:00	Lupo	yorick	50000	5000000						3	0.168
2010-03-09T20:18:00	Wolfgang Fluck	C91F72025	50000	5000000						3	0.168
2011-07-07T03:34:00	S36049	Wolle5	50000	5000000						3	0.168
2012-12-01T08:12:00	he4var		50000	5000000						3	0.168
2013-10-14T20:59:00	arnaud	SPR14	50000	5000000						3	0.168
2014-04-30T07:18:00	Chang Chia-Tche	exbpc13	50000	5000000						3	0.168
2015-02-18T00:22:00	codest	aliyun	50000	5000000						3	0.168
2015-08-24T02:45:00	Chang Chia-Tche	exbpc13	50000	5000000						3	0.168
2015-12-13T20:44:16	Bruce	Desk7	50000	5000000	41711097608582628662729	75.143	2	2		2	0.112
2019-09-23T15:15:29	TJAOI	Manual testing	50000	5000000						222	12.42

date	userid	compid	res64	spent (GHz-days)
1998-10-29T00:00:00	ANONYMOUS	v4_computers	7321837571C67678	0.070
2015-07-01T17:36:00	MadPoo	Manual testing	7321837571C67678	0.070

date

userid

compid

res64

spent (GHz-days)

1998-10-29T00:00:00

ANONYMOUS

v4_computers

7321837571C67678

0.070

2015-07-01T17:36:00

MadPoo

Manual testing

7321837571C67678

0.070

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 = 200000000 (P-1 stage 2)

B1 = 10000000 (P-1 stage 1)

B1 = 950000, B2 = 27550000 (P-1 stage 2)

B1 = 950000 (P-1 stage 1)

B1 = 80000, B2 = 1380000 (P-1 stage 2)

B1 = 80000 (P-1 stage 1)

B1 = 20000, B2 = 300000 (P-1 stage 2)

B1 = 20000 (P-1 stage 1)

10³

10⁴

10⁵

10⁶

10⁷

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

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