M1481113 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	20.0619	68.6567%	500000	15000000	0.0714	4.9408%	20.1333	70.2053%	1.5486%
PrimeNet	2⁵⁷	0.0130	63.1579%	6000	100000	0.0006	2.2807%	0.0136	63.9982%	0.8403%
GPU72	2⁶¹	0.2074	65.5738%	6000	50000	0.0005	0.9452%	0.2079	65.8992%	0.3254%
Difference	+6	+19.8545	+3.0829%	+494000	+14950000	+0.0710	+3.9956%	+19.9254	+4.3061%	+4.3061%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

20.0619

68.6567%

500000

15000000

0.0714

4.9408%

20.1333

70.2053%

1.5486%

PrimeNet

2⁵⁷

0.0130

63.1579%

6000

100000

0.0006

2.2807%

0.0136

63.9982%

0.8403%

GPU72

2⁶¹

0.2074

65.5738%

6000

50000

0.0005

0.9452%

0.2079

65.8992%

0.3254%

Difference

+19.8545

+3.0829%

+494000

+14950000

+0.0710

+3.9956%

+19.9254

+4.3061%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1481113	686110786121	12	39.320	231620 2² × 5 × 37 × 313	-	37	313	5.608e-8	2.881e-6	4.169e-6
1481113	57813527863921	14	45.716	19516920 2³ × 3 × 5 × 162641	2008-09-30	8	162641	4.562e-6	0.0005	0.0009
1481113	38330032882063582433503	23	75.021	12939604500825927 3³ × 53 × 3907 × 2314397531	2018-10-06	3907	2314397531	10,162	6.9810	13.038

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

1481113

686110786121

39.320

231620
2² × 5 × 37 × 313

313

5.608e-8

2.881e-6

4.169e-6

1481113

57813527863921

45.716

19516920
2³ × 3 × 5 × 162641

2008-09-30

162641

4.562e-6

0.0005

0.0009

1481113

38330032882063582433503

75.021

12939604500825927
3³ × 53 × 3907 × 2314397531

2018-10-06

3907

2314397531

10,162

6.9810

13.038

exponent	prime factors	composite factor	digits	bits*
1481113	686110786121 57813527863921	39666485051143175223440441	26	85.036
1481113	686110786121 38330032882063582433503	26298648992756423824156229537811863	35	114.341
1481113	57813527863921 38330032882063582433503	2215994424052191076241303594615345263	37	120.737
1481113	686110786121 57813527863921 38330032882063582433503	1520417676326201449652421855191357641006763494823	49	160.057

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2016-03-17T19:14:54	alpertron	Manual testing	500000	15000000	12	-	skipped known factor: 686110786121 skipped known factor: 57813527863921	-	-	0.071	-	-	4.941%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2008-09-30T13:29:00	markr	Manual testing	?	?	57813527863921	45.716	14	1.39738e-6	0.128	3.15816e-6

ECM factoring results:

Old Calculation Method

Total ECM effort:	26.547 GHz-days
Estimated T-Level:	25.391

Digits	B1	Curves	Complete	FacMiss
20	11000	301 / 100	3.010	4.855%
25	50000	301 / 280	1.075	34.064%
30	250000	50 / 640	0.078	92.479%

New Calculation Method

Total ECM effort:	26.547 GHz-days
Estimated T-Level:	25.391

Digits	B1	Complete	FacMiss
20	11000	12.263	0.000%
25	50000	1.390	24.916%
30	250000	0.116	89.004%
35	1000000	0.008	99.198%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		248	11.78
50000	5000000	38330032882063582433503	3	0.143
250000	40000000		50	14.62

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2017-11-24T14:22:09	Chang Chia-Tche	exbpc13	50000	5000000						3	0.143
2018-10-06T04:52:17	Chang Chia-Tche	exbpc13	50000	5000000	38330032882063582433503	75.021	3	2		3	0.143
2019-04-12T15:23:32	TJAOI	Manual testing	50000	5000000						245	11.64
2022-04-21T11:50:00	TJAOI	Manual testing	250000	40000000						50	14.62

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-01T06:26:45

Oliver Kruse

GTX-1

686110786121

57813527863921

3788A2F80084C8__

2017-10-28T13:29:40

kkmrkkblmbrbk

old

686110786121

57813527863921

3788A2F80084C8__

2018-10-06T11:47:00

Oliver Kruse

GTX-2

686110786121

57813527863921

38330032882063582433503

670E0809A9945C__

2018-10-07T08:45:33

pew

laptop

686110786121

57813527863921

38330032882063582433503

670E0809A9945C__

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 = 500000, B2 = 15000000 (P-1 stage 2)

B1 = 500000 (P-1 stage 1)

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

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