M3075869 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	2⁶⁸	19.3782	67.6471%	3075869	217752150	1.8230	9.0326%	21.2013	70.5694%	2.9223%
PrimeNet	2⁶⁰	0.0499	63.3333%	12000	220000	0.0029	2.5267%	0.0528	64.2598%	0.9265%
GPU72	2⁶⁴	1.1572	65.6250%	14000	220000	0.0031	1.4674%	1.1603	66.1294%	0.5044%
Difference	+4	+18.2210	+2.0221%	+3061869	+217532150	+1.8199	+7.5652%	+20.0410	+4.4399%	+4.4399%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁸

19.3782

67.6471%

3075869

217752150

1.8230

9.0326%

21.2013

70.5694%

2.9223%

PrimeNet

2⁶⁰

0.0499

63.3333%

12000

220000

0.0029

2.5267%

0.0528

64.2598%

0.9265%

GPU72

2⁶⁴

1.1572

65.6250%

14000

220000

0.0031

1.4674%

1.1603

66.1294%

0.5044%

Difference

+18.2210

+2.0221%

+3061869

+217532150

+1.8199

+7.5652%

+20.0410

+4.4399%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
3075869	1058910965417	13	39.946	172132 2² × 23 × 1871	-	23	1871	2.995e-8	1.526e-5	2.355e-5
3075869	23184266204124108658447	23	74.296	3768734332334067 3 × 1256244777444689	2018-07-09	3	1256244777444689	1,331.9	8,446,711	15,776,103

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

3075869

1058910965417

39.946

172132
2² × 23 × 1871

1871

2.995e-8

1.526e-5

2.355e-5

3075869

23184266204124108658447

74.296

3768734332334067
3 × 1256244777444689

2018-07-09

1256244777444689

1,331.9

8,446,711

15,776,103

exponent	prime factors	composite factor	digits	bits*
3075869	1058910965417 23184266204124108658447	24550073708693785886400721481927399	35	114.241

exponent

prime factors

composite factor

digits

bits*

3075869

1058910965417
23184266204124108658447

24550073708693785886400721481927399

114.241

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2021-03-05T06:43:11	Jocelyn Larouche	Manual testing	307586	3383455	6	-	skipped known factor: 1058910965417	-	-	0.059	-	-	3.376%
2021-03-05T18:37:46	Jocelyn Larouche	Manual testing	307586	6459324	6	-	skipped known factor: 1058910965417	-	-	0.079	-	-	3.897%
2021-06-22T11:14:23	Jocelyn Larouche	Manual testing	3075869	3075869		-	skipped known factor: 1058910965417	-	-	0.380	-	-	3.738%
2021-12-19T18:06:23	Jocelyn Larouche	Manual testing	3075869	108997350		-	skipped known factor: 1058910965417	-	-	1.092	-	-	8.164%
2022-01-03T11:29:02	Jocelyn Larouche	Manual testing	3075869	217752150		-	skipped known factor: 1058910965417	-	-	1.823	-	-	9.033%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2021-06-19T04:13:04	Jocelyn Larouche	Manual testing	2⁶⁷	2⁶⁸		-	-	9.72	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	0.350 GHz-days
Estimated T-Level:	0.150

Digits	B1	Curves	Complete	FacMiss
20	11000	3 / 100	0.030	97.030%
25	50000	3 / 280	0.011	98.932%

New Calculation Method

Total ECM effort:	0.350 GHz-days
Estimated T-Level:	0.150

Digits	B1	Complete	FacMiss
20	11000	0.115	89.102%
25	50000	0.011	98.938%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000	23184266204124108658447	3	0.350

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2018-07-09T15:55:02	ATH	ec2-ECMCF	50000	5000000	23184266204124108658447	74.296	3	2		3	0.350

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-29T01:30:36

Oliver Kruse

GTX-1

1058910965417

B6BA00FE9D6347__

2017-12-11T09:00:51

kkmrkkblmbrbk

c4.xlarge

1058910965417

B6BA00FE9D6347__

2018-07-11T15:43:10

Oliver Kruse

GTX-6

1058910965417

23184266204124108658447

B6BA00FE9D6347__

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 = 3075869, B2 = 217752150 (P-1 stage 2)

B1 = 3075869, B2 = 108997350 (P-1 stage 2)

B1 = 3075869 (P-1 stage 1)

B1 = 307586, B2 = 6459324 (P-1 stage 2)

B1 = 307586, B2 = 3383455 (P-1 stage 2)

B1 = 307586 (P-1 stage 1)

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

10¹²

10¹³

10¹⁴

10¹⁵

10¹⁶

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