M1045507 Mersenne number exponent details

Residue

Status

L-L

3203F69673458306

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	28.4206	70.1493%	300000	10000000	0.0356	4.0878%	28.4562	71.3695%	1.2203%
PrimeNet	2⁵⁶	0.0092	64.2857%	4500	60000	0.0003	1.9572%	0.0095	64.9847%	0.6990%
GPU72	2⁶⁰	0.1469	66.6667%	4500	18000	0.0002	0.6170%	0.1471	66.8723%	0.2057%
Difference	+7	+28.2737	+3.4826%	+295500	+9982000	+0.0354	+3.4708%	+28.3091	+4.4972%	+4.4972%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

28.4206

70.1493%

300000

10000000

0.0356

4.0878%

28.4562

71.3695%

1.2203%

PrimeNet

2⁵⁶

0.0092

64.2857%

4500

60000

0.0003

1.9572%

0.0095

64.9847%

0.6990%

GPU72

2⁶⁰

0.1469

66.6667%

4500

18000

0.0002

0.6170%

0.1471

66.8723%

0.2057%

Difference

+28.2737

+3.4826%

+295500

+9982000

+0.0354

+3.4708%

+28.3091

+4.4972%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1045507	3529663684258001702647	22	71.580	1688015328571689 3 × 13² × 3329418794027	2009-08-08	169	3329418794027	743.32	7,795.7	14,560

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

1045507

3529663684258001702647

71.580

1688015328571689
3 × 13² × 3329418794027

2009-08-08

169

3329418794027

743.32

7,795.7

14,560

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	10000	90000		-		-	-	0.001	-	-	0.475%
2016-03-17T18:59:34	alpertron	Manual testing	300000	10000000	12	-		-	-	0.036	-	-	4.088%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1999-07-04T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁶		-	-	0.009	-	-
2001-11-14T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁷		-	-	0.018	-	-
2003-03-27T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.037	-	-
2022-03-07T17:30:27	LordJulius	Manual testing	2⁵⁸	2⁶⁰		-	-	0.110	-	-
2009-02-15T23:10:00	Sturle Sunde	interavia.ifi	2⁶⁰	2⁶¹		-	-	0.147	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	17.446 GHz-days
Estimated T-Level:	25.344

Digits	B1	Curves	Complete	FacMiss
20	11000	323 / 100	3.230	3.892%
25	50000	323 / 280	1.154	31.486%
30	250000	44 / 640	0.069	93.351%

New Calculation Method

Total ECM effort:	17.446 GHz-days
Estimated T-Level:	25.344

Digits	B1	Complete	FacMiss
20	11000	14.731	0.000%
25	50000	1.613	19.937%
30	250000	0.131	87.717%
35	1000000	0.009	99.131%

ECM Summary

B1	B2	factor	curves	GHz-days
		3529663684258001702647	1	0.00000e+0
50000	5000000		279	9.75
250000	25000000		44	7.692

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2007-09-23T13:52:00	Chad Davis	Bayes	50000	5000000						1	0.035
2008-02-23T15:50:00	Steve Scott	Abit-3	50000	5000000						3	0.105
2008-12-02T07:54:00	Sturle Sunde	v23	50000	5000000						3	0.105
2009-03-24T18:41:00	Sturle Sunde	v23	50000	5000000						3	0.105
2009-08-08T15:48:00	SubPrime	c2d0			3529663684258001702647	71.580		1		1	-
2017-02-03T18:32:25	TJAOI	Manual testing	50000	5000000						128	4.475
2017-11-24T16:08:08	TJAOI	Manual testing	50000	5000000						141	4.930
2020-03-30T08:09:18	TJAOI	Manual testing	250000	25000000						44	7.692

date	userid	compid	res64	spent (GHz-days)
2003-08-25T00:00:00	ANONYMOUS	v4_computers	3203F69673458306	0.031

date

userid

compid

res64

spent (GHz-days)

2003-08-25T00:00:00

ANONYMOUS

v4_computers

3203F69673458306

0.031

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-28T19:55:55

Oliver Kruse

GTX-2

3529663684258001702647

6277D5363EF4B5__

2017-10-15T22:27:50

Oliver Kruse

Threadripper

3529663684258001702647

6277D5363EF4B5__

2017-12-27T10:22:27

ATH

ec2-1xf

3529663684258001702647

6277D5363EF4B5__

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

B1 = 300000 (P-1 stage 1)

B1 = 10000, B2 = 90000 (P-1 stage 2)

B1 = 10000 (P-1 stage 1)

10¹

10²

10³

10⁴

10⁵

10⁶

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

10¹²

10¹³

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