M4259 Mersenne number exponent details

Residue

Status

L-L

-unknown-

-unknown-

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	6,976.7357	80.5970%	1000000000	201000000000	0.8572	16.8079%	6,977.5930	83.8582%	16.3582%
PrimeNet	2⁴⁰	0.0000	67.5000%	500	10000	0.0000	2.4294%	0.0000	68.2896%	0.7896%
GPU72	2⁴⁴	0.0006	70.4545%	500	10000	0.0000	0.9685%	0.0006	70.7407%	0.2861%
Difference	+23	+6,976.7352	+10.1425%	+999999500	+200999990000	+0.8572	+15.8394%	+6,977.5924	+13.1176%	+13.1176%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

6,976.7357

80.5970%

1000000000

201000000000

0.8572

16.8079%

6,977.5930

83.8582%

16.3582%

PrimeNet

2⁴⁰

0.0000

67.5000%

500

10000

0.0000

2.4294%

0.0000

68.2896%

0.7896%

GPU72

2⁴⁴

0.0006

70.4545%

500

10000

0.0000

0.9685%

0.0006

70.7407%

0.2861%

Difference

+23

+6,976.7352

+10.1425%

+999999500

+200999990000

+0.8572

+15.8394%

+6,977.5924

+13.1176%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
4259	918648240952126271	18	59.672	107847879895765 5 × 17 × 1811 × 700606619	2009-10-25	1811	700606619	20.471	0.0028	0.0051
4259	484399053828087857927777245183883458323463	42	138.475	56867698265800405955362437800408952609 3³ × 13 × 162016234375499732066559651853016959	2020-09-30	27	162016234375499732066559651853016959	3.644e+13	6.361e+23	1.188e+24

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

4259

918648240952126271

59.672

107847879895765
5 × 17 × 1811 × 700606619

2009-10-25

1811

700606619

20.471

0.0028

0.0051

4259

484399053828087857927777245183883458323463

138.475

56867698265800405955362437800408952609
3³ × 13 × 162016234375499732066559651853016959

2020-09-30

162016234375499732066559651853016959

3.644e+13

6.361e+23

1.188e+24

exponent	prime factors	composite factor	digits	bits*
4259	918648240952126271 484399053828087857927777245183883458323463	44499233871804723804798818062937535112954630212722 2737996473	60	198.148

exponent

prime factors

composite factor

digits

bits*

4259

918648240952126271
484399053828087857927777245183883458323463

44499233871804723804798818062937535112954630212722
2737996473

198.148

	GHz-Days	worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved
2021-07-05T07:00:06	ViliamF	3	1000000000	201000000000		-		-	-	0.857	-	-	16.808%

GHz-Days

worth

Factor
probability

date

userid

compid

stage

factor

digits

bits*

spent

saved

2021-07-05T07:00:06

ViliamF

1000000000

201000000000

0.857

-

-

16.808%

	Bits	Factor	GHz-Days	worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved
2009-10-25T00:00:00	Carsten Kossendey	v4_computers	?	?	918648240952126271	59.672	18	2.439	4.96621e-7	5.724

Bits

Factor

GHz-Days

worth

date

userid

compid

from

factor

bits*

digits

spent

saved

2009-10-25T00:00:00

Carsten Kossendey

v4_computers

918648240952126271

59.672

2.439

4.96621e-7

5.724

ECM factoring results:

Old Calculation Method

Total ECM effort:	17.937 GHz-days
Estimated T-Level:	33.807

Digits	B1	Curves	Complete	FacMiss
20	11000	1304 / 100	13.040	0.000%
25	50000	1304 / 280	4.657	0.941%
30	250000	1304 / 640	2.038	13.015%
35	1000000	1203 / 1580	0.761	46.690%
40	3000000	1203 / 4700	0.256	77.415%
45	11000000	418 / 9700	0.043	95.782%
50	44000000	201 / 17100	0.012	98.831%

New Calculation Method

Total ECM effort:	17.937 GHz-days
Estimated T-Level:	33.807

Digits	B1	Complete	FacMiss
20	11000	288.517	0.000%
25	50000	82.863	0.000%
30	250000	19.156	0.000%
35	1000000	3.812	2.211%
40	3000000	0.664	51.491%
45	11000000	0.105	90.009%
50	44000000	0.015	98.484%
55	110000000	0.002	99.793%

ECM Summary

B1	B2	factor	curves	GHz-days
3000000	300000000		785	2.442
11000000	11000000		101	0.781
11000000	1100000000		217	2.475
44000000	4400000000		200	9.125
110000000	900514153782	484399053828087857927777245183883458323463	1	3.114

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-05-19T07:59:00	unconnected	E5430-next	44000000	4400000000						200	9.125
2009-10-13T13:28:00	Carsten Kossendey	durandal	3000000	300000000						1	0.003
2010-06-17T18:28:00	James Hintz	12_052810	3000000	300000000						100	0.311
2010-06-17T20:59:00	James Hintz	12_052810	3000000	300000000						100	0.311
2010-06-17T23:31:00	James Hintz	12_052810	3000000	300000000						100	0.311
2010-06-18T02:03:00	James Hintz	12_052810	3000000	300000000						100	0.311
2010-06-18T04:34:00	James Hintz	12_052810	3000000	300000000						100	0.311
2010-06-18T07:05:00	James Hintz	12_052810	3000000	300000000						100	0.311
2010-06-18T09:37:00	James Hintz	12_052810	3000000	300000000						100	0.311
2010-06-18T11:46:00	James Hintz	12_052810	3000000	300000000						84	0.261
2011-01-02T02:44:00	James Hintz	OMFG	11000000	1100000000						3	0.034
2011-01-14T02:29:00	James Hintz	OMFG	11000000	1100000000						3	0.034
2011-01-29T03:04:00	James Hintz	OMFG	11000000	1100000000						11	0.125
2016-10-02T17:38:07	kkmrkkblmbrbk	kel1	11000000	11000000						101	0.781
2020-03-18T05:20:01	James Hintz	work_lappy_5_16_2019	11000000	1100000000						100	1.141
2020-05-29T13:22:32	James Hintz	work_lappy_5_16_2019	11000000	1100000000						100	1.141
2020-09-30T15:48:42	Ryan Propper	Manual testing	110000000	900514153782	484399053828087857927777245183883458323463	138.475	1	2	7921730607498746562	1	3.114

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-21T18:33:47

Oliver Kruse

Oliver-PC

918648240952126271

0548EAC5F9087B__

2017-09-21T19:21:11

Oliver Kruse

Manual testing

918648240952126271

0548EAC5F9087B__

2017-10-12T13:52:42

kkmrkkblmbrbk

Manual testing

918648240952126271

0548EAC5F9087B__

2020-04-17T12:32:21

Oliver Kruse

IOS-1

918648240952126271

791F2DA8E1540E__

2020-10-01T03:45:38

tottenhoff

3-of-4-Ryzen-5-3600

918648240952126271

484399053828087857927777245183883458323463

791F2DA8E1540E40

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 = 1000000000, B2 = 201000000000 (P-1 stage 2)

B1 = 1000000000 (P-1 stage 1)

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

10¹²

10¹³

10¹⁴

10¹⁵

10¹⁶

10¹⁷

10¹⁸

10¹⁹

10²⁰

10²¹

10²²

10²³

10²⁴

10²⁵

10²⁶

10²⁷

10²⁸

10²⁹

10³⁰

10³¹

10³²

10³³

10³⁴

10³⁵

10³⁶

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