M3628267 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	16.4279	67.6471%	100000	130364850	1.0961	5.3932%	17.5240	69.3919%	1.7449%
PrimeNet	2⁶⁰	0.0423	63.3333%	16000	320000	0.0050	3.0732%	0.0473	64.4602%	1.1268%
GPU72	2⁶⁴	0.9810	65.6250%	22000	400000	0.0065	2.0340%	0.9875	66.3242%	0.6992%
Difference	+4	+15.4469	+2.0221%	+78000	+129964850	+1.0896	+3.3592%	+16.5365	+3.0677%	+3.0677%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁸

16.4279

67.6471%

100000

130364850

1.0961

5.3932%

17.5240

69.3919%

1.7449%

PrimeNet

2⁶⁰

0.0423

63.3333%

16000

320000

0.0050

3.0732%

0.0473

64.4602%

1.1268%

GPU72

2⁶⁴

0.9810

65.6250%

22000

400000

0.0065

2.0340%

0.9875

66.3242%

0.6992%

Difference

+15.4469

+2.0221%

+78000

+129964850

+1.0896

+3.3592%

+16.5365

+3.0677%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
3628267	816462102942007033	18	59.502	112514060148 2² × 3 × 7 × 103 × 281 × 46279	-	281	46279	0.0354	0.0004	0.0007
3628267	76927855287681637793	20	66.060	10601184434288 2⁴ × 7 × 37 × 1733 × 1476169	2019-09-19	1733	1476169	5.8429	0.0125	0.0229

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

3628267

816462102942007033

59.502

112514060148
2² × 3 × 7 × 103 × 281 × 46279

281

46279

0.0354

0.0004

0.0007

3628267

76927855287681637793

66.060

10601184434288
2⁴ × 7 × 37 × 1733 × 1476169

2019-09-19

1733

1476169

5.8429

0.0125

0.0229

exponent	prime factors	composite factor	digits	bits*
3628267	816462102942007033 76927855287681637793	62808678502998945413877761951964598169	38	125.562

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2022-03-19T09:21:33	Lisander Viaene	Manual testing	100000	100000		-	skipped known factor: 816462102942007033	-	-	0.015	-	-	0.881%
2022-03-20T23:03:36	Lisander Viaene	Desktop	100000	38206140		-	skipped known factor: 816462102942007033 skipped known factor: 76927855287681637793	-	-	0.331	-	-	4.497%
2022-05-20T02:44:07	Jocelyn Larouche	Manual testing	100000	130364850		-	skipped known factor: 816462102942007033 skipped known factor: 76927855287681637793	-	-	1.096	-	-	5.393%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2019-09-19T11:52:03	TJAOI	Manual testing	2⁶⁶	2⁶⁷*	76927855287681637793	66.060	20	1.772	0.775	3.604
2022-03-13T12:30:45	Jocelyn Larouche	Manual testing	2⁶⁷	2⁶⁸		-	-	8.238	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	0.445 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:	0.445 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		3	0.445

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2018-11-09T08:03:11	rucio		50000	5000000						3	0.445

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-11-10T20:48:02

Oliver Kruse

GTX-3

816462102942007033

3760C666C466D9__

2017-12-18T20:54:24

kkmrkkblmbrbk

c4.xlarge

816462102942007033

3760C666C466D9__

2019-09-20T08:51:26

mnd9

office

816462102942007033

76927855287681637793

3760C666C466D96C

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 = 100000, B2 = 130364850 (P-1 stage 2)

B1 = 100000, B2 = 38206140 (P-1 stage 2)

B1 = 100000 (P-1 stage 1)

10¹

10²

10³

10⁴

10⁵

10¹

10²

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