M1508413 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	19.6988	68.6567%	500000	15000000	0.0835	4.9517%	19.7823	70.2088%	1.5520%
PrimeNet	2⁵⁷	0.0127	63.1579%	6500	100000	0.0008	2.3430%	0.0135	64.0211%	0.8632%
GPU72	2⁶¹	0.2036	65.5738%	6000	50000	0.0005	0.9491%	0.2042	65.9005%	0.3268%
Difference	+6	+19.4951	+3.0829%	+494000	+14950000	+0.0830	+4.0026%	+19.5782	+4.3082%	+4.3082%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

19.6988

68.6567%

500000

15000000

0.0835

4.9517%

19.7823

70.2088%

1.5520%

PrimeNet

2⁵⁷

0.0127

63.1579%

6500

100000

0.0008

2.3430%

0.0135

64.0211%

0.8632%

GPU72

2⁶¹

0.2036

65.5738%

6000

50000

0.0005

0.9491%

0.2042

65.9005%

0.3268%

Difference

+19.4951

+3.0829%

+494000

+14950000

+0.0830

+4.0026%

+19.5782

+4.3082%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1508413	1865296525814159	16	50.728	618297683 179 × 293 × 11789	-	293	11789	0.0002	5.954e-5	7.767e-5
1508413	9156171398089596824833	22	72.955	3035034635106432 2⁷ × 3 × 7 × 29 × 199 × 195651559	2019-05-17	199	195651559	1,072.1	0.6904	1.2895

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

1508413

1865296525814159

50.728

618297683
179 × 293 × 11789

293

11789

0.0002

5.954e-5

7.767e-5

1508413

9156171398089596824833

72.955

3035034635106432
2⁷ × 3 × 7 × 29 × 199 × 195651559

2019-05-17

199

195651559

1,072.1

0.6904

1.2895

exponent	prime factors	composite factor	digits	bits*
1508413	1865296525814159 9156171398089596824833	17078974698615495945309256666634210447	38	123.684

exponent

prime factors

composite factor

digits

bits*

1508413

1865296525814159
9156171398089596824833

17078974698615495945309256666634210447

123.684

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2016-03-17T19:15:38	alpertron	Manual testing	500000	15000000	12	-	skipped known factor: 1865296525814159	-	-	0.084	-	-	4.952%

ECM factoring results:

Old Calculation Method

Total ECM effort:	30.079 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:	30.079 GHz-days
Estimated T-Level:	25.391

Digits	B1	Complete	FacMiss
20	11000	14.654	0.000%
25	50000	1.651	19.189%
30	250000	0.141	86.866%
35	1000000	0.010	99.021%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		104	5.798
50000	5000000	9156171398089596824833	147	8.195
250000	35000000		50	16.09

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2017-11-28T05:51:05	Oliver Kruse	HTC5	50000	5000000						3	0.167
2018-10-30T15:54:55	Chang Chia-Tche	exbpc13	50000	5000000						3	0.167
2019-05-17T12:26:01	TJAOI	Manual testing	50000	5000000	9156171398089596824833	72.955	147	2		147	8.195
2019-05-17T12:26:01	TJAOI	Manual testing	50000	5000000						98	5.463
2022-03-17T11:20:44	TJAOI	Manual testing	250000	35000000						50	16.09

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-01T11:03:38

Oliver Kruse

GTX-3

1865296525814159

7385B86A6225A4__

2017-10-29T10:39:04

kkmrkkblmbrbk

c4.xlarge

1865296525814159

7385B86A6225A4__

2019-05-17T13:57:19

ATH

ec2-PRPCF

1865296525814159

9156171398089596824833

636B90FA8E788E6E

2019-05-23T04:07:16

kracker

GRID-11

1865296525814159

9156171398089596824833

636B90FA8E788E6E

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)

10¹

10²

10³

10⁴

10⁵

10⁶

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