M30137 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	985.9614	77.6119%	200000000	5000000000	0.3686	12.3281%	986.3300	80.3720%	2.7600%
PrimeNet	2⁴⁰	0.0000	62.5000%	500	10000	0.0000	4.1083%	0.0000	64.0406%	1.5406%
GPU72	2⁴⁴	0.0001	65.9091%	500	10000	0.0000	1.7609%	0.0001	66.5094%	0.6003%
Difference	+23	+985.9613	+11.7028%	+199999500	+4999990000	+0.3686	+10.5672%	+986.3299	+13.8626%	+13.8626%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

985.9614

77.6119%

200000000

5000000000

0.3686

12.3281%

986.3300

80.3720%

2.7600%

PrimeNet

2⁴⁰

0.0000

62.5000%

500

10000

0.0000

4.1083%

0.0000

64.0406%

1.5406%

GPU72

2⁴⁴

0.0001

65.9091%

500

10000

0.0000

1.7609%

0.0001

66.5094%

0.6003%

Difference

+23

+985.9613

+11.7028%

+199999500

+4999990000

+0.3686

+10.5672%

+986.3299

+13.8626%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
30137	245769022063478761487	21	67.736	4077529648994239 7591609 × 537110071	2014-04-23	7591609	537110071	1,956.1	0.0291	0.0437
30137	371287533331608494808531049098097	33	108.194	6159994912094908166183280504 2³ × 3 × 2315177 × 110862562417742217373	2017-09-25	2315177	110862562417742217373	5.986e+12	4.824e+9	9.010e+9

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

30137

245769022063478761487

67.736

4077529648994239
7591609 × 537110071

2014-04-23

7591609

537110071

1,956.1

0.0291

0.0437

30137

371287533331608494808531049098097

108.194

6159994912094908166183280504
2³ × 3 × 2315177 × 110862562417742217373

2017-09-25

2315177

110862562417742217373

5.986e+12

4.824e+9

9.010e+9

exponent	prime factors	composite factor	digits	bits*
30137	245769022063478761487 371287533331608494808531049098097	91250973971270694227438491313487101949665985928590 239	53	175.930

exponent

prime factors

composite factor

digits

bits*

30137

245769022063478761487
371287533331608494808531049098097

91250973971270694227438491313487101949665985928590
239

175.930

	GHz-Days	worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved
2016-10-06T09:36:58	kkmrkkblmbrbk	Manual testing	200000000	5000000000	12	-	skipped known factor: 245769022063478761487	-	-	0.369	-	-	12.328%

GHz-Days

worth

Factor
probability

date

userid

compid

stage

factor

digits

bits*

spent

saved

2016-10-06T09:36:58

kkmrkkblmbrbk

Manual testing

200000000

5000000000

skipped known factor: 245769022063478761487

0.369

-

-

12.328%

	Bits	Factor	GHz-Days	worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved
1999-10-21T00:00:00	ANONYMOUS	v4_computers	2⁵²	2⁵³		-	-	0.020	-	-

Bits

Factor

GHz-Days

worth

date

userid

compid

from

factor

bits*

digits

spent

saved

1999-10-21T00:00:00

ANONYMOUS

v4_computers

2⁵²

2⁵³

0.020

-

-

ECM factoring results:

Old Calculation Method

Total ECM effort:	23.489 GHz-days
Estimated T-Level:	31.994

Digits	B1	Curves	Complete	FacMiss
20	11000	1499 / 100	14.990	0.000%
25	50000	1499 / 280	5.354	0.469%
30	250000	1214 / 640	1.897	14.981%
35	1000000	630 / 1580	0.399	67.108%
40	3000000	619 / 4700	0.132	87.659%

New Calculation Method

Total ECM effort:	23.489 GHz-days
Estimated T-Level:	31.994

Digits	B1	Complete	FacMiss
20	11000	183.232	0.000%
25	50000	37.658	0.000%
30	250000	6.591	0.137%
35	1000000	0.967	38.010%
40	3000000	0.121	88.643%
45	11000000	0.013	98.703%
50	44000000	0.001	99.875%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		285	0.164
250000	25000000		584	1.678
1000000	100000000		11	0.126
3000000	300000000		413	14.24
3000000	300000000	371287533331608494808531049098097	87	3.000
3000000	339000000		98	3.522
3000000	341549937		7	0.252
3000000	345407014		7	0.253
3000000	348000000		7	0.254

ECM Details

										GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-03-29T23:56:00	Matthias Wurtinger	WUR_E6600	50000	5000000						30	0.017
2010-04-13T14:10:00	James Hintz	OMFG	50000	5000000						11	0.006
2010-04-19T03:55:00	James Hintz	home2	50000	5000000						101	0.058
2010-04-20T15:13:00	James Hintz	05_122109	50000	5000000						11	0.006
2010-04-20T16:22:00	James Hintz	05_122109	50000	5000000						11	0.006
2010-04-20T17:38:00	James Hintz	05_122109	50000	5000000						11	0.006
2010-04-20T19:11:00	James Hintz	05_122109	50000	5000000						11	0.006
2010-04-20T20:36:00	James Hintz	05_122109	50000	5000000						11	0.006
2010-04-20T21:35:00	James Hintz	05_122109	50000	5000000						11	0.006
2010-04-20T22:37:00	James Hintz	05_122109	50000	5000000						11	0.006
2010-04-20T23:39:00	James Hintz	05_122109	50000	5000000						11	0.006
2010-04-21T00:42:00	James Hintz	05_122109	50000	5000000						11	0.006
2010-04-21T01:44:00	James Hintz	05_122109	50000	5000000						11	0.006
2010-04-21T02:46:00	James Hintz	05_122109	50000	5000000						11	0.006
2010-04-21T03:48:00	James Hintz	05_122109	50000	5000000						11	0.006
2010-04-21T04:51:00	James Hintz	05_122109	50000	5000000						11	0.006
2011-01-19T15:51:00	James Hintz	NEW_OMFG	250000	25000000						11	0.032
2011-03-18T10:58:00	James Hintz	17_051310	250000	25000000						11	0.032
2014-12-10T01:55:00	James Hintz	08_04_2014	250000	25000000						562	1.615
2014-12-10T02:21:00	James Hintz	08_04_2014	1000000	100000000						11	0.126
2017-09-25T18:52:08	nordi	nordiputer	3000000	300000000	371287533331608494808531049098097	108.194	87	2		87	3.000
2017-09-29T17:19:58	nordi	nordiputer	3000000	300000000						413	14.24
2022-05-14T12:06:24	Luminescence	Tyrant	3000000	339000000						7	0.252
2022-05-14T12:11:29	Luminescence	Tyrant	3000000	339000000						7	0.252
2022-05-14T12:17:08	Luminescence	Tyrant	3000000	339000000						7	0.252
2022-05-14T12:21:46	Luminescence	Tyrant	3000000	339000000						7	0.252
2022-05-14T12:24:19	Luminescence	Tyrant	3000000	339000000						7	0.252
2022-05-14T12:44:02	Luminescence	Tyrant	3000000	339000000						7	0.252
2022-05-14T12:57:32	Luminescence	Tyrant	3000000	339000000						7	0.252
2022-05-14T13:05:26	Luminescence	Tyrant	3000000	339000000						7	0.252
2022-05-14T13:37:53	Luminescence	Tyrant	3000000	341549937						7	0.252
2022-05-14T13:44:43	Luminescence	Tyrant	3000000	339000000						7	0.252
2022-05-14T14:24:54	Luminescence	Tyrant	3000000	339000000						7	0.252
2022-05-14T14:26:37	Luminescence	Tyrant	3000000	339000000						7	0.252
2022-05-14T15:04:32	Luminescence	Tyrant	3000000	339000000						7	0.252
2022-05-14T15:39:51	Luminescence	Tyrant	3000000	339000000						7	0.252
2022-05-14T15:59:18	Luminescence	Tyrant	3000000	339000000						7	0.252
2022-05-15T04:53:19	Luminescence	Tyrant	3000000	345407014						7	0.253
2022-05-15T05:27:19	Luminescence	Tyrant	3000000	348000000						7	0.254

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