M346627 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	85.7230	71.6418%	50000	50000	0.0007	0.4111%	85.7237	71.7584%	0.1166%
PrimeNet	2⁴⁰	0.0000	52.5000%	3400	100000	0.0001	16.2485%	0.0001	60.2180%	7.7180%
GPU72	2⁴⁴	0.0000	56.8182%	6000	170000	0.0002	12.0272%	0.0002	62.0118%	5.1936%
Difference	+23	+85.7230	+14.8236%	+44000	-120000	+0.0005	-11.6161%	+85.7235	+9.7466%	+9.7466%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

85.7230

71.6418%

50000

0.0007

0.4111%

85.7237

71.7584%

0.1166%

PrimeNet

2⁴⁰

0.0000

52.5000%

3400

100000

0.0001

16.2485%

0.0001

60.2180%

7.7180%

GPU72

2⁴⁴

0.0000

56.8182%

6000

170000

0.0002

12.0272%

0.0002

62.0118%

5.1936%

Difference

+23

+85.7230

+14.8236%

+44000

-120000

+0.0005

-11.6161%

+85.7235

+9.7466%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
346627	585799631	9	29.126	845 5 × 13²	-	169	169	2.441e-10	2.376e-6	4.835e-6
346627	352803583255463	15	48.326	508909553 508909553	2014-04-02	1	508909553	0.0002	0.3898	0.7280
346627	273085481348485628339519	24	77.854	393918363757707317 31 × 81068263 × 156744989	2015-02-06	81068263	156744989	163,170	1.1975	2.3192

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

346627

585799631

29.126

845
5 × 13²

169

2.441e-10

2.376e-6

4.835e-6

346627

352803583255463

48.326

508909553
508909553

2014-04-02

508909553

0.0002

0.3898

0.7280

346627

273085481348485628339519

77.854

393918363757707317
31 × 81068263 × 156744989

2015-02-06

81068263

156744989

163,170

1.1975

2.3192

exponent	prime factors	composite factor	digits	bits*
346627	585799631 352803583255463	206672208886528004134153	24	77.452
346627	585799631 273085481348485628339519	159973374205400263490093372917489	33	106.980
346627	352803583255463 273085481348485628339519	96345536354788637623916827769075542297	38	126.180
346627	585799631 352803583255463 273085481348485628339519	56439179645132269003083194481815005888707492407	47	155.305

	GHz-Days	worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved
2022-02-06T16:56:57	Lisander Viaene	Manual testing	50000	50000		-	skipped known factor: 585799631	-	-	0.001	-	-	0.411%

GHz-Days

worth

Factor
probability

date

userid

compid

stage

factor

digits

bits*

spent

saved

2022-02-06T16:56:57

Lisander Viaene

Manual testing

50000

skipped known factor: 585799631

0.001

-

-

0.411%

	Bits	Factor	GHz-Days	worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved
2014-04-02T10:45:00	TJAOI	Manual testing	?	?	352803583255463	48.326	15	6.30573e-5	0.007	0.000

Bits

Factor

GHz-Days

worth

date

userid

compid

from

factor

bits*

digits

spent

saved

2014-04-02T10:45:00

TJAOI

Manual testing

352803583255463

48.326

6.30573e-5

0.007

0.000

ECM factoring results:

Old Calculation Method

Total ECM effort:	10.471 GHz-days
Estimated T-Level:	26.125

Digits	B1	Curves	Complete	FacMiss
20	11000	425 / 100	4.250	1.396%
25	50000	425 / 280	1.518	21.859%
30	250000	144 / 640	0.225	79.838%

New Calculation Method

Total ECM effort:	10.471 GHz-days
Estimated T-Level:	26.125

Digits	B1	Complete	FacMiss
20	11000	23.899	0.000%
25	50000	3.028	4.840%
30	250000	0.287	75.049%
35	1000000	0.022	97.832%
40	3000000	0.001	99.860%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		231	2.416
50000	5000000	273085481348485628339519	50	0.523
250000	25000000		144	7.532

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2014-10-03T12:41:00	TJAOI	Manual testing	50000	5000000						50	0.523
2015-02-06T11:15:00	TJAOI	Manual testing	50000	5000000						0	-
2015-02-06T11:15:00	TJAOI	Manual testing	50000	5000000	273085481348485628339519	77.854	50	2		50	0.523
2015-12-11T11:31:28	TJAOI	Manual testing	50000	5000000						90	0.941
2016-04-22T16:24:05	TJAOI	Manual testing	50000	5000000						91	0.952
2017-11-17T15:41:50	TJAOI	Manual testing	250000	25000000						44	2.301
2019-10-21T11:35:06	TJAOI	Manual testing	250000	25000000						100	5.230

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-22T23:25:39

Oliver Kruse

Ollaptop

31E23AAADD239E__

2017-09-23T17:11:32

Oliver Kruse

Manual testing

31E23AAADD239E__

2017-10-13T04:30:40

Oliver Kruse

GTX-1

31E23AAADD239E__

2017-12-13T07:49:07

ATH

xps

585799631

352803583255463

273085481348485628339519

31E23AAADD239E__

2020-04-18T15:13:58

Oliver Kruse

AddPrpType5

585799631

352803583255463

273085481348485628339519

03823BE6DAA075__

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 = 50000 (P-1 stage 1)

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁰

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