M29453 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	1,008.8588	77.6119%	500000000	10000000000	0.8128	13.6817%	1,009.6715	80.6750%	3.0631%
PrimeNet	2⁴⁰	0.0000	62.5000%	500	10000	0.0000	4.0843%	0.0000	64.0316%	1.5316%
GPU72	2⁴⁴	0.0001	65.9091%	500	10000	0.0000	1.7491%	0.0001	66.5054%	0.5963%
Difference	+23	+1,008.8587	+11.7028%	+499999500	+9999990000	+0.8128	+11.9326%	+1,009.6715	+14.1696%	+14.1696%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

1,008.8588

77.6119%

500000000

10000000000

0.8128

13.6817%

1,009.6715

80.6750%

3.0631%

PrimeNet

2⁴⁰

0.0000

62.5000%

500

10000

0.0000

4.0843%

0.0000

64.0316%

1.5316%

GPU72

2⁴⁴

0.0001

65.9091%

500

10000

0.0000

1.7491%

0.0001

66.5054%

0.5963%

Difference

+23

+1,008.8587

+11.7028%

+499999500

+9999990000

+0.8128

+11.9326%

+1,009.6715

+14.1696%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
29453	909882918841458193	18	59.658	15446353832232 2³ × 3 × 53 × 20533 × 591407	2014-04-23	20533	591407	3.5284	4.124e-5	4.807e-5
29453	55874828857083921356896681927	29	95.496	948542234357856947626671 3 × 7 × 431 × 15199 × 26813 × 41179 × 6244877	2008-08-26	41179	6244877	5.089e+11	0.0003	0.0005
29453	655998538733547377507059917477748097	36	118.981	11136361978975781372136283527616 2⁶ × 23 × 359 × 4523 × 4659233679013937482229	2017-11-03	4523	4659233679013937482229	4.678e+12	2.028e+11	3.787e+11

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

29453

909882918841458193

59.658

15446353832232
2³ × 3 × 53 × 20533 × 591407

2014-04-23

20533

591407

3.5284

4.124e-5

4.807e-5

29453

55874828857083921356896681927

95.496

948542234357856947626671
3 × 7 × 431 × 15199 × 26813 × 41179 × 6244877

2008-08-26

41179

6244877

5.089e+11

0.0003

0.0005

29453

655998538733547377507059917477748097

118.981

11136361978975781372136283527616
2⁶ × 23 × 359 × 4523 × 4659233679013937482229

2017-11-03

4523

4659233679013937482229

4.678e+12

2.028e+11

3.787e+11

exponent	prime factors	composite factor	digits	bits*
29453	909882918841458193 55874828857083921356896681927	50839552370250455859361764090585013047989177911	47	155.155
29453	909882918841458193 655998538733547377507059917477748097	59688186517861145735074252807247212147086207741080 8721	54	178.640
29453	55874828857083921356896681927 655998538733547377507059917477748097	36653806082234097530200904050745135795489242792035 067675238542919	65	214.477
29453	909882918841458193 55874828857083921356896681927 655998538733547377507059917477748097	33350672064751954052404904814678619881412385739239 330325397624615846892810574685367	83	274.136

	GHz-Days	worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved
2017-01-04T01:58:22	kkmrkkblmbrbk	Manual testing	500000000	10000000000	12	-	skipped known factor: 909882918841458193 skipped known factor: 55874828857083921356896681927	-	-	0.813	-	-	13.682%

GHz-Days

worth

Factor
probability

date

userid

compid

stage

factor

digits

bits*

spent

saved

2017-01-04T01:58:22

kkmrkkblmbrbk

Manual testing

500000000

10000000000

skipped known factor: 909882918841458193
skipped known factor: 55874828857083921356896681927

0.813

-

-

13.682%

date	userid	compid	b1	b2	start	factor	Smooth	digits	bits*	ghz-days
2021-05-10T09:47:11	ATH	colab-Pp1	100000000	10000000000	2	7			-	-	0.544

date

userid

compid

start

factor

Smooth

digits

bits*

ghz-days

2021-05-10T09:47:11

ATH

colab-Pp1

100000000

10000000000

0.544

	Bits	Factor	GHz-Days	worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved
2009-10-25T00:00:00	GrunwalderGIMP	v4_computers	?	?	909882918841458193	59.658	18	0.921	3.32601e-5	1.888

Bits

Factor

GHz-Days

worth

date

userid

compid

from

factor

bits*

digits

spent

saved

2009-10-25T00:00:00

GrunwalderGIMP

v4_computers

909882918841458193

59.658

0.921

3.32601e-5

1.888

ECM factoring results:

Old Calculation Method

Total ECM effort:	19.204 GHz-days
Estimated T-Level:	31.617

Digits	B1	Curves	Complete	FacMiss
20	11000	1249 / 100	12.490	0.000%
25	50000	1249 / 280	4.461	1.146%
30	250000	1126 / 640	1.759	17.192%
35	1000000	511 / 1580	0.323	72.360%
40	3000000	500 / 4700	0.106	89.907%

New Calculation Method

Total ECM effort:	19.204 GHz-days
Estimated T-Level:	31.617

Digits	B1	Complete	FacMiss
20	11000	156.789	0.000%
25	50000	31.892	0.000%
30	250000	5.500	0.409%
35	1000000	0.797	45.062%
40	3000000	0.098	90.620%
45	11000000	0.011	98.944%
50	44000000	0.001	99.899%

ECM Summary

B1	B2	factor	curves	GHz-days
		55874828857083921356896681927	1	0.00000e+0
50000	5000000		123	0.071
250000	25000000		615	1.767
1000000	100000000		11	0.126
3000000	300000000		386	13.31
3000000	300000000	655998538733547377507059917477748097	114	3.931

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2008-08-26T19:59:00	ANONYMOUS	Manual testing			55874828857083921356896681927	95.496		1		1	-
2009-04-04T14:31:00	Matthias Wurtinger	WUR_E6600	50000	5000000						30	0.017
2009-05-10T17:33:00	Matthias Wurtinger	WUR_E6600	250000	25000000						30	0.086
2009-10-15T05:57:00	GrunwalderGIMP	GWPrime02	50000	5000000						93	0.053
2011-01-19T18:12:00	James Hintz	NEW_OMFG	250000	25000000						11	0.032
2011-03-19T03:27:00	James Hintz	17_051310	250000	25000000						11	0.032
2014-12-03T06:46:00	James Hintz	08_04_2014	250000	25000000						563	1.618
2014-12-03T07:14:00	James Hintz	08_04_2014	1000000	100000000						11	0.126
2017-11-03T08:30:08	nordi	nordiputer	3000000	300000000	655998538733547377507059917477748097	118.981	114	2		114	3.931
2017-11-05T15:28:51	nordi	nordiputer	3000000	300000000						386	13.31

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-21T19:39:34

Oliver Kruse

Ollaptop

92B6BD229EEAD6__

2017-09-21T21:38:46

Oliver Kruse

Manual testing

92B6BD229EEAD6__

2017-10-02T10:29:36

kkmrkkblmbrbk

Manual testing

909882918841458193

55874828857083921356896681927

92B6BD229EEAD6__

2017-11-03T13:57:38

alpertron

laptop2

909882918841458193

55874828857083921356896681927

655998538733547377507059917477748097

3924B4710D8E26__

2017-11-03T22:56:12

Oliver Kruse

GTX-0

909882918841458193

55874828857083921356896681927

655998538733547377507059917477748097

3924B4710D8E26__

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 = 500000000, B2 = 10000000000 (P-1 stage 2)

B1 = 500000000 (P-1 stage 1)

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

10¹²

10¹³

10¹⁴

10¹⁵

10¹⁶

10¹⁷

10¹⁸

10¹⁹

10²⁰

10²¹

10²²

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