M2298731 Mersenne number exponent details

Residue

Status

L-L

3365BFFC6CD36502

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	2⁶⁸	25.9295	67.6471%	500000	10000000	0.0997	4.3692%	26.0291	69.0606%	1.4136%
PrimeNet	2⁵⁸	0.0167	62.0690%	10000	190000	0.0019	2.9277%	0.0186	63.1795%	1.1105%
GPU72	2⁶²	0.2673	64.5161%	12000	200000	0.0022	1.7373%	0.2694	65.1326%	0.6165%
Difference	+6	+25.6622	+3.1309%	+488000	+9800000	+0.0975	+2.6318%	+25.7597	+3.9280%	+3.9280%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁸

25.9295

67.6471%

500000

10000000

0.0997

4.3692%

26.0291

69.0606%

1.4136%

PrimeNet

2⁵⁸

0.0167

62.0690%

10000

190000

0.0019

2.9277%

0.0186

63.1795%

1.1105%

GPU72

2⁶²

0.2673

64.5161%

12000

200000

0.0022

1.7373%

0.2694

65.1326%

0.6165%

Difference

+25.6622

+3.1309%

+488000

+9800000

+0.0975

+2.6318%

+25.7597

+3.9280%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2298731	22751366863431242830832659009	29	94.200	4948679698370806073184 2⁵ × 3² × 1409 × 304501 × 40049503927	2020-08-02	304501	40049503927	2.956e+9	213.77	399.21

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

2298731

22751366863431242830832659009

94.200

4948679698370806073184
2⁵ × 3² × 1409 × 304501 × 40049503927

2020-08-02

304501

40049503927

2.956e+9

213.77

399.21

	GHz-Days	worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved
2003-08-08T00:00:00	ANONYMOUS	v4_computers	2048	204800		-		-	-	0.001	-	-	0.229%
2010-10-20T20:14:00	Oscar Östlin		75011	75011		-		-	-	0.007	-	-	0.679%
2011-01-17T15:41:00	Oscar Östlin		90000	1755000		-		-	-	0.018	-	-	2.267%
2013-11-16T02:26:00	c10ck3r	Manual testing	500000	10000000		-		-	-	0.100	-	-	4.369%

GHz-Days

worth

Factor
probability

date

userid

compid

stage

factor

digits

bits*

spent

saved

2003-08-08T00:00:00

ANONYMOUS

v4_computers

2048

204800

0.001

-

-

0.229%

2010-10-20T20:14:00

Oscar Östlin

75011

0.007

-

-

0.679%

2011-01-17T15:41:00

Oscar Östlin

90000

1755000

0.018

-

-

2.267%

2013-11-16T02:26:00

c10ck3r

Manual testing

500000

10000000

0.100

-

-

4.369%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2016-02-23T16:29:11	Mark Rose	Manual testing	2¹	2⁶⁰		-	-	0.067	-	-
2009-01-14T01:52:00	Sturle Sunde	aalto.ifi	2⁶⁰	2⁶¹		-	-	0.067	-	-
2012-05-12T08:48:00	Sebastian Hornbostel	Manual testing	2⁶¹	2⁶²		-	-	0.134	-	-
2013-12-06T02:46:00	Jerry Hallett	Manual testing	2⁶²	2⁶³		-	-	0.427	-	-
2015-03-12T10:50:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.854	-	-
2015-03-12T10:50:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.625	-	-
2015-11-04T09:56:28	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	3.251	-	-
2017-05-27T13:18:47	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	6.502	-	-
2019-03-18T11:45:41	TJAOI	Manual testing	2⁶⁷	2⁶⁸		-	-	13.00	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	7.521 GHz-days
Estimated T-Level:	4.250

Digits	B1	Curves	Complete	FacMiss
20	11000	85 / 100	0.850	42.559%
25	50000	85 / 280	0.304	73.778%

New Calculation Method

Total ECM effort:	7.521 GHz-days
Estimated T-Level:	4.250

Digits	B1	Complete	FacMiss
20	11000	2.742	6.445%
25	50000	0.248	78.051%
30	250000	0.015	98.486%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		84	7.432
50000	5000000	22751366863431242830832659009	1	0.088

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-01-15T05:02:00	oodaira	Win02	50000	5000000						3	0.265
2010-01-07T18:48:00	Chang Chia-Tche	sekhmet	50000	5000000						3	0.265
2011-11-18T18:38:00	Bud	annan	50000	5000000						3	0.265
2013-09-21T06:46:00	arnaud	srv-630	50000	5000000						3	0.265
2015-04-12T10:19:00	Jason U	Server7	50000	5000000						3	0.265
2016-02-13T18:57:05	Sintax	cloud2	50000	5000000						3	0.265
2016-04-17T20:45:57	Bruce	Desk6	50000	5000000						3	0.265
2016-08-04T22:13:58	Bruce	Desk6	50000	5000000						3	0.265
2017-01-05T05:14:32	Bruce	Desk6	50000	5000000						3	0.265
2017-08-16T00:28:01	Bruce	Desk6	50000	5000000						3	0.265
2018-01-17T15:49:29	Bruce	Desk6	50000	5000000						3	0.265
2018-07-15T04:10:37	Bruce	Desk6	50000	5000000						3	0.265
2019-10-10T18:02:10	monsted	rootweiler	50000	5000000						3	0.265
2020-03-07T08:54:22	Corey	Computer	50000	5000000						3	0.265
2020-03-13T16:53:38	Brett Walker	brain	50000	5000000						3	0.265
2020-03-21T20:25:38	mnd9	colab2	50000	5000000						3	0.265
2020-04-02T20:00:51	mnd9	colab2	50000	5000000						3	0.265
2020-04-16T06:21:22	nranks	wlaptop	50000	5000000						3	0.265
2020-04-25T07:13:28	EricP	Cannonfodder	50000	5000000						3	0.265
2020-05-03T08:39:46	EricP	Cannonfodder	50000	5000000						3	0.265
2020-05-15T21:54:12	mnd9	75203b	50000	5000000						3	0.265
2020-06-01T13:18:53	mnd9	kitchen	50000	5000000						3	0.265
2020-06-21T03:48:28	MarkS	desktop-i7	50000	5000000						3	0.265
2020-07-01T09:27:04	mnd9	libproj	50000	5000000						3	0.265
2020-07-07T17:38:34	GAN	LMS-15	50000	5000000						3	0.265
2020-07-13T22:33:55	GAN	LMS-04	50000	5000000						3	0.265
2020-07-20T08:42:50	mnd9	50871b	50000	5000000						3	0.265
2020-07-26T09:04:22	GAN	LMS-13	50000	5000000						3	0.265
2020-08-02T16:47:48	GAN	LMS-13	50000	5000000	22751366863431242830832659009	94.200	1	2	3689823363750850	1	0.088

date	userid	compid	res64	spent (GHz-days)
1999-02-21T00:00:00	ANONYMOUS	v4_computers	3365BFFC6CD36502	0.155
2018-04-30T07:56:40	kkmrkkblmbrbk	old	3365BFFC6CD36502	0.155

date

userid

compid

res64

spent (GHz-days)

1999-02-21T00:00:00

ANONYMOUS

v4_computers

3365BFFC6CD36502

0.155

2018-04-30T07:56:40

kkmrkkblmbrbk

old

3365BFFC6CD36502

0.155

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 = 500000, B2 = 10000000 (P-1 stage 2)

B1 = 500000 (P-1 stage 1)

B1 = 90000, B2 = 1755000 (P-1 stage 2)

B1 = 90000 (P-1 stage 1)

B1 = 75011 (P-1 stage 1)

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

B1 = 2048 (P-1 stage 1)

10²

10³

10⁴

10⁵

10⁶

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

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