M600451 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	unknown	1000000	30000000	0.0568	39.9716%	0.0568	39.9716%	39.9716%
PrimeNet	2⁴⁰	0.0000	50.0000%	6000	220000	0.0004	20.5188%	0.0004	60.2594%	10.2594%
GPU72	2⁴⁴	0.0000	54.5455%	10000	360000	0.0006	15.4295%	0.0006	61.5589%	7.0134%
Difference	-44	0.0000	-54.5455%	+990000	+29640000	+0.0562	+24.5420%	+0.0562	-21.5873%	-21.5873%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

unknown

1000000

30000000

0.0568

39.9716%

0.0568

39.9716%

PrimeNet

2⁴⁰

0.0000

50.0000%

6000

220000

0.0004

20.5188%

0.0004

60.2594%

10.2594%

GPU72

2⁴⁴

0.0000

54.5455%

10000

360000

0.0006

15.4295%

0.0006

61.5589%

7.0134%

Difference

-44

0.0000

-54.5455%

+990000

+29640000

+0.0562

+24.5420%

+0.0562

-21.5873%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
600451	317038129	9	28.240	264 2³ × 3 × 11	-	8	11	6.296e-11	1.799e-7	3.587e-7
600451	3179857802039503818870301367	28	91.361	2647891170170008725833 13 × 31 × 181 × 199 × 182416212381569	2020-08-01	199	182416212381569	1.355e+9	218,965	408,966

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

600451

317038129

28.240

264
2³ × 3 × 11

6.296e-11

1.799e-7

3.587e-7

600451

3179857802039503818870301367

91.361

2647891170170008725833
13 × 31 × 181 × 199 × 182416212381569

2020-08-01

199

182416212381569

1.355e+9

218,965

408,966

exponent	prime factors	composite factor	digits	bits*
600451	317038129 3179857802039503818870301367	1008136168044656674822995239059822343	37	119.601

exponent

prime factors

composite factor

digits

bits*

600451

317038129
3179857802039503818870301367

1008136168044656674822995239059822343

119.601

	GHz-Days	worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved
2016-03-17T18:48:47	alpertron	Manual testing	1000000	30000000	12	-	skipped known factor: 317038129	-	-	0.057	-	-	31.459%

GHz-Days

worth

Factor
probability

date

userid

compid

stage

factor

digits

bits*

spent

saved

2016-03-17T18:48:47

alpertron

Manual testing

1000000

30000000

skipped known factor: 317038129

0.057

-

-

31.459%

ECM factoring results:

Old Calculation Method

Total ECM effort:	17.525 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:	17.525 GHz-days
Estimated T-Level:	26.125

Digits	B1	Complete	FacMiss
20	11000	21.065	0.000%
25	50000	2.590	7.504%
30	250000	0.242	78.521%
35	1000000	0.018	98.191%
40	3000000	0.001	99.885%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		281	4.761
250000	25000000		44	3.727
250000	25000000	3179857802039503818870301367	68	5.760
250000	40000000		32	3.277

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2014-08-30T06:51:00	Richard B. Woods	Puttputt	50000	5000000						10	0.169
2015-08-21T09:48:00	TJAOI	Manual testing	50000	5000000						90	1.525
2016-04-08T13:18:53	TJAOI	Manual testing	50000	5000000						90	1.525
2016-09-02T12:16:00	TJAOI	Manual testing	50000	5000000						91	1.542
2018-07-27T12:40:12	TJAOI	Manual testing	250000	25000000						44	3.727
2020-08-01T17:36:23	nordi	sweet16	250000	25000000	3179857802039503818870301367	91.361	68	2	7322759573329650	68	5.760
2022-05-05T09:28:56	TJAOI	Manual testing	250000	40000000						32	3.277

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-27T12:14:46

Oliver Kruse

GTX-3

317038129

03ECE91F9C8FC7__

2017-09-28T09:43:54

Oliver Kruse

Manual testing

317038129

03ECE91F9C8FC7__

2017-11-09T03:44:44

kkmrkkblmbrbk

c4.large

317038129

03ECE91F9C8FC7__

2020-04-19T13:09:35

Oliver Kruse

AddPrpType5

317038129

B2C80F3368F88A__

2020-08-02T08:30:46

ANONYMOUS

dory

317038129

3179857802039503818870301367

B2C80F3368F88A1F

2020-08-06T12:55:43

nordi

sweet16

317038129

3179857802039503818870301367

B2C80F3368F88A1F

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 = 1000000, B2 = 30000000 (P-1 stage 2)

B1 = 1000000 (P-1 stage 1)

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

10¹²

10¹³

10¹⁴

10¹⁵

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