M3507029 Mersenne number exponent details

Residue

Status

L-L

-unknown-

-unknown-

PRP

35F60BC7CE61423E

verified PRP

	Trial Factoring	P-1 Factoring	Combined
Limit	GHz-days	Probability	B1	B2	GHz-days	Probability	GHz-days	Probability	Prob over default TF
Actual	2⁷²	272.6905	69.4444%	4000000	150000000	1.8206	6.4119%	274.5111	71.4036%	1.9592%
PrimeNet	2⁶⁰	0.0438	63.3333%	15000	300000	0.0046	2.9615%	0.0484	64.4192%	1.0859%
GPU72	2⁶⁴	1.0149	65.6250%	20000	360000	0.0059	1.9161%	1.0208	66.2837%	0.6587%
Difference	+8	+271.6756	+3.8194%	+3980000	+149640000	+1.8147	+4.4958%	+273.4903	+5.1200%	+5.1200%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁷²

272.6905

69.4444%

4000000

150000000

1.8206

6.4119%

274.5111

71.4036%

1.9592%

PrimeNet

2⁶⁰

0.0438

63.3333%

15000

300000

0.0046

2.9615%

0.0484

64.4192%

1.0859%

GPU72

2⁶⁴

1.0149

65.6250%

20000

360000

0.0059

1.9161%

1.0208

66.2837%

0.6587%

Difference

+271.6756

+3.8194%

+3980000

+149640000

+1.8147

+4.4958%

+273.4903

+5.1200%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
3507029	123808830164103219107795353	27	86.678	17651526429365599644 2² × 3² × 78367 × 80671 × 77558447	2021-09-16	80671	77558447	6,058,710	0.6551	1.2019

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

3507029

123808830164103219107795353

86.678

17651526429365599644
2² × 3² × 78367 × 80671 × 77558447

2021-09-16

80671

77558447

6,058,710

0.6551

1.2019

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2009-07-04T06:46:00	Carsten Kossendey	leela	20000	240000		-		-	-	0.005	-	-	0.510%
2011-11-08T01:22:00	markr	tiny	235000	5875000		-		-	-	0.083	-	-	2.425%
2021-09-16T08:34:50	mikr	MSI	4000000	150000000	12		123808830164103219107795353	27	86.678	1.821	0.737	3.641	6.412%
2022-04-23T18:01:26	Jocelyn Larouche	Manual testing	1000000	145208700		-	skipped known factor: 123808830164103219107795353	-	-	1.349	-	-	5.486%

date	userid	compid	b1	b2	start	factor	Smooth	digits	bits*	ghz-days
2021-08-26T13:47:15	ArtyomP	axioo	50000	2500000	2	7			-	-	0.032
2021-08-26T14:09:40	ArtyomP	axioo	50000	2500000	6	5			-	-	0.032

date

userid

compid

start

factor

Smooth

digits

bits*

ghz-days

2021-08-26T13:47:15

ArtyomP

axioo

50000

2500000

0.032

2021-08-26T14:09:40

ArtyomP

axioo

50000

2500000

0.032

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2016-02-23T16:29:31	Mark Rose	Manual testing	2¹	2⁶⁰		-	-	0.044	-	-
2009-02-20T14:01:00	Jayson King	atlas	2⁶⁰	2⁶¹		-	-	0.044	-	-
2011-07-16T01:16:00	Grant McCracken	thumper	2⁶¹	2⁶²		-	-	0.088	-	-
2012-06-20T01:19:00	GrunwalderGIMP	Manual testing	2¹	2⁶³		-	-	0.455	-	-
2016-02-23T16:29:31	Mark Rose	Manual testing	2⁶²	2⁶³		-	-	0.280	-	-
2015-01-25T20:43:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.560	-	-
2015-01-25T20:43:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.065	-	-
2016-03-04T09:43:19	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	2.131	-	-
2017-01-07T17:26:13	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	4.262	-	-
2018-12-10T15:07:49	TJAOI	Manual testing	2⁶⁷	2⁶⁸		-	-	8.523	-	-
2021-01-15T12:32:04	axn	Manual testing	2⁶⁸	2⁶⁹		-	-	17.05	-	-
2021-03-17T11:32:43	-Anonymous-	Manual testing	2⁶⁹	2⁷⁰		-	-	34.09	-	-
2021-03-17T11:32:43	-Anonymous-	Manual testing	2⁷⁰	2⁷¹		-	-	68.19	-	-
2021-03-19T11:33:25	-Anonymous-	Manual testing	2⁷¹	2⁷²		-	-	136.4	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	5.473 GHz-days
Estimated T-Level:	1.800

Digits	B1	Curves	Complete	FacMiss
20	11000	36 / 100	0.360	69.641%
25	50000	36 / 280	0.129	87.915%

New Calculation Method

Total ECM effort:	5.473 GHz-days
Estimated T-Level:	1.800

Digits	B1	Complete	FacMiss
20	11000	1.177	30.824%
25	50000	0.107	89.880%
30	250000	0.007	99.344%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		29	4.277
50000	6750000		7	1.197

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-07-08T15:42:00	zampel	malissol	50000	5000000						3	0.442
2012-03-17T11:53:00	Lukasz Wrobel	u-w	50000	5000000						3	0.442
2015-06-17T15:54:00	Bruce	desk16	50000	5000000						3	0.442
2017-02-02T23:18:09	Dennis Schreiber	z400	50000	5000000						3	0.442
2019-08-02T10:53:14	furkell	furkell1	50000	5000000						3	0.442
2021-05-03T04:39:11	tonyw	Worke	50000	5000000						7	1.032
2021-06-17T14:40:54	kutens	terra	50000	6750000						7	1.197
2021-08-03T18:03:40	GAN	KL-SCH02	50000	5000000						7	1.032

date	userid	compid	res64	spent (GHz-days)
1999-10-07T00:00:00	ANONYMOUS	v4_computers	E4CECF0BE86FB4__	0.368

date

userid

compid

res64

spent (GHz-days)

1999-10-07T00:00:00

ANONYMOUS

v4_computers

E4CECF0BE86FB4__

0.368

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 = 4000000, B2 = 150000000 (P-1 stage 2)

B1 = 1000000, B2 = 145208700 (P-1 stage 2)

B1 = 4000000 (P-1 stage 1)

B1 = 1000000 (P-1 stage 1)

B1 = 235000, B2 = 5875000 (P-1 stage 2)

B1 = 235000 (P-1 stage 1)

B1 = 20000, B2 = 240000 (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