M193873 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	153.2649	73.1343%	100000000	2000000000	1.3607	12.3031%	154.6256	76.4396%	3.3053%
PrimeNet	2⁴⁰	0.0000	55.0000%	2000	50000	0.0000	12.4275%	0.0000	60.5924%	5.5924%
GPU72	2⁴⁴	0.0000	59.0909%	3600	80000	0.0001	8.8197%	0.0001	62.6990%	3.6080%
Difference	+23	+153.2648	+14.0434%	+99996400	+1999920000	+1.3607	+3.4834%	+154.6255	+13.7407%	-0.3027%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

153.2649

73.1343%

100000000

2000000000

1.3607

12.3031%

154.6256

76.4396%

3.3053%

PrimeNet

2⁴⁰

0.0000

55.0000%

2000

50000

0.0000

12.4275%

0.0000

60.5924%

5.5924%

GPU72

2⁴⁴

0.0000

59.0909%

3600

80000

0.0001

8.8197%

0.0001

62.6990%

3.6080%

Difference

+23

+153.2648

+14.0434%

+99996400

+1999920000

+1.3607

+3.4834%

+154.6255

+13.7407%

-0.3027%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
193873	5816191	7	22.472	15 3 × 5	-	3	5	2.891e-12	2.079e-8	4.082e-8
193873	814751670247	12	39.568	2101251 3 × 17 × 41201	2008-07-27	17	41201	6.861e-7	1.512e-5	2.803e-5
193873	215307694529183281	18	57.579	555280246680 2³ × 3 × 5 × 4627335389	2014-07-28	8	4627335389	0.1569	1.6856	3.1483
193873	60540296379601077793144673	26	85.646	156133903069537990832 2⁴ × 17 × 13711 × 41865779480821	2019-05-23	13711	41865779480821	70,090,862	15,251	28,484

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

193873

5816191

22.472

15
3 × 5

2.891e-12

2.079e-8

4.082e-8

193873

814751670247

39.568

2101251
3 × 17 × 41201

2008-07-27

41201

6.861e-7

1.512e-5

2.803e-5

193873

215307694529183281

57.579

555280246680
2³ × 3 × 5 × 4627335389

2014-07-28

4627335389

0.1569

1.6856

3.1483

193873

60540296379601077793144673

85.646

156133903069537990832
2⁴ × 17 × 13711 × 41865779480821

2019-05-23

13711

41865779480821

70,090,862

15,251

28,484

exponent	prime factors	composite factor	digits	bits*
193873	5816191 814751670247	4738751331725569177	19	62.039
193873	5816191 215307694529183281	1252270675151385036302671	25	80.051
193873	814751670247 215307694529183281	175422303734682942479537540407	30	97.147
193873	5816191 60540296379601077793144673	352113926940368372250787908800543	33	108.118
193873	5816191 814751670247 215307694529183281	1020289624180929317903003926677329737	37	119.618
193873	814751670247 60540296379601077793144673	49325307592528385271526003093260644231	38	125.214
193873	215307694529183281 60540296379601077793144673	13034791639605369370426308369726599365812113	44	143.225
193873	5816191 814751670247 60540296379601077793144673	286885410091895261660782095456994719630544121	45	147.685
193873	5816191 215307694529183281 60540296379601077793144673	75812837821147992883949160903228519692042119321583	50	165.697
193873	814751670247 215307694529183281 60540296379601077793144673	10620118259690106370504209590665022444038830016334 301911	56	182.793
193873	5816191 814751670247 215307694529183281 60540296379601077793144673	61768636240945259461169249283339587553816646791533 419766041001	62	205.264

exponent

prime factors

composite factor

digits

bits*

193873

5816191
814751670247

4738751331725569177

62.039

193873

5816191
215307694529183281

1252270675151385036302671

80.051

193873

814751670247
215307694529183281

175422303734682942479537540407

97.147

193873

5816191
60540296379601077793144673

352113926940368372250787908800543

108.118

193873

5816191
814751670247
215307694529183281

1020289624180929317903003926677329737

119.618

193873

814751670247
60540296379601077793144673

49325307592528385271526003093260644231

125.214

193873

215307694529183281
60540296379601077793144673

13034791639605369370426308369726599365812113

143.225

193873

5816191
814751670247
60540296379601077793144673

286885410091895261660782095456994719630544121

147.685

193873

5816191
215307694529183281
60540296379601077793144673

75812837821147992883949160903228519692042119321583

165.697

193873

814751670247
215307694529183281
60540296379601077793144673

10620118259690106370504209590665022444038830016334
301911

182.793

193873

5816191
814751670247
215307694529183281
60540296379601077793144673

61768636240945259461169249283339587553816646791533
419766041001

205.264

	GHz-Days	worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved
2017-08-23T17:03:34	kkmrkkblmbrbk	Manual testing	100000000	2000000000	12	-	skipped known factor: 5816191 skipped known factor: 814751670247	-	-	1.361	-	-	12.303%

GHz-Days

worth

Factor
probability

date

userid

compid

stage

factor

digits

bits*

spent

saved

2017-08-23T17:03:34

kkmrkkblmbrbk

Manual testing

100000000

2000000000

skipped known factor: 5816191
skipped known factor: 814751670247

1.361

-

-

12.303%

date	userid	compid	b1	b2	start	factor	Smooth	digits	bits*	ghz-days
2019-05-23T10:49:35	YarBer	Manual testing	10000000	10000000	3	3	60540296379601077793144673	P+1	26	85.646	0.005
2021-07-11T08:33:17	ATH	ec2-P_1	15000000	1500000000	2	7			-	-	0.586

date

userid

compid

start

factor

Smooth

digits

bits*

ghz-days

2019-05-23T10:49:35

YarBer

Manual testing

10000000

60540296379601077793144673

P+1

85.646

0.005

2021-07-11T08:33:17

ATH

ec2-P_1

15000000

1500000000

0.586

	Bits	Factor	GHz-Days	worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved
2008-07-27T10:50:00	J Feitsma	Manual testing	?	?	814751670247	39.568	12	3.08341e-7	0.002	6.40480e-7

Bits

Factor

GHz-Days

worth

date

userid

compid

from

factor

bits*

digits

spent

saved

2008-07-27T10:50:00

J Feitsma

Manual testing

814751670247

39.568

3.08341e-7

0.002

6.40480e-7

ECM factoring results:

Total ECM effort:	11.608 GHz-days
Estimated T-Level:	28.568

Digits	B1	Complete	FacMiss
20	11000	48.880	0.000%
25	50000	6.889	0.102%
30	250000	0.714	48.983%
35	1000000	0.058	94.357%
40	3000000	0.004	99.615%

ECM Summary

B1	B2	factor	curves	GHz-days
		215307694529183281	1	0.00000e+0
50000	5000000		281	1.370
250000	25000000		388	9.461
250000	31250000		7	0.185
250000	36000000		14	0.391
250000	38500000		7	0.201

ECM Details

										GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2014-07-28T13:48:00	TJAOI	Manual testing	50000	5000000						50	0.244
2014-07-28T14:53:00	TJAOI	Manual testing			215307694529183281	57.579		1		1	-
2014-12-12T13:35:00	TJAOI	Manual testing	50000	5000000						50	0.244
2015-05-29T10:14:00	TJAOI	Manual testing	50000	5000000						90	0.439
2016-03-24T20:20:14	TJAOI	Manual testing	50000	5000000						91	0.444
2017-07-14T09:28:03	TJAOI	Manual testing	250000	25000000						44	1.073
2019-04-21T21:34:50	happy5214	Cosmic	250000	25000000						3	0.073
2019-04-26T10:28:24	TJAOI	Manual testing	250000	25000000						100	2.438
2019-11-29T12:31:34	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.073
2019-11-30T10:16:53	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.073
2019-12-01T09:28:03	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.073
2019-12-02T09:55:35	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.073
2019-12-03T12:21:20	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.073
2019-12-04T14:38:03	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.073
2019-12-05T22:18:20	Ducho_YYZ	oracleJP	250000	25000000						3	0.073
2019-12-06T19:23:09	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.073
2019-12-07T23:00:36	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.073
2019-12-08T21:57:32	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.073
2019-12-09T21:24:09	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.073
2019-12-10T21:29:41	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.073
2019-12-11T21:33:20	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.073
2019-12-13T00:18:34	kracker	O0	250000	25000000						3	0.073
2019-12-15T00:03:46	Eisenprimus	cheap_and_old	250000	25000000						3	0.073
2019-12-15T01:19:55	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.073
2019-12-16T08:28:17	Ducho_YYZ	oracleDE2	250000	25000000						3	0.073
2019-12-17T06:23:35	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.073
2019-12-18T10:44:53	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.073
2019-12-19T15:41:58	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.073
2019-12-21T02:41:57	Ducho_YYZ	oracleSW	250000	25000000						3	0.073
2019-12-22T11:15:19	Ducho_YYZ	oracleAU2	250000	25000000						3	0.073
2019-12-24T09:28:07	_p95holder_	TFL18_PRPt12pE_m	250000	25000000						3	0.073
2019-12-25T00:37:37	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.073
2019-12-27T00:04:56	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.073
2019-12-28T21:55:37	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.073
2019-12-30T19:55:02	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.073
2020-01-01T19:53:23	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.073
2020-01-03T23:00:29	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.073
2020-01-06T00:48:24	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.073
2020-01-08T06:10:50	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.073
2020-01-10T09:38:05	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.073
2020-01-12T15:14:13	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.073
2020-01-14T19:41:10	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.073
2020-01-17T00:12:17	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.073
2020-01-19T07:51:26	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.073
2020-01-21T16:48:28	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.073
2020-01-23T23:56:26	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.073
2020-01-26T10:07:24	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.073
2020-01-29T00:00:27	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.073
2020-01-31T17:49:06	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.073
2020-02-03T17:49:54	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.073
2020-02-06T21:11:18	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.073
2020-02-10T05:50:17	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.073
2020-02-13T19:05:01	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.073
2020-02-18T11:27:12	_p95holder_	TFL18_PRPt12pE_m	250000	25000000						3	0.073
2020-02-20T18:36:51	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.073
2020-02-24T15:00:13	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.073
2020-02-27T20:57:06	MarkS	laptop64	250000	25000000						3	0.073
2020-03-02T19:39:17	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.073
2020-03-07T19:54:15	-Anonymous-	aws-nano	250000	25000000						3	0.073
2020-03-13T12:07:49	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.073
2020-03-19T01:30:44	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.073
2020-04-01T14:03:27	-Anonymous-	aws-nano	250000	25000000						3	0.073
2020-04-16T11:08:58	Oliver Kruse	Melissa	250000	25000000						3	0.073
2020-04-30T14:54:08	Greg	azure2	250000	25000000						3	0.073
2020-05-04T20:59:14	Greg Hogan	azure2	250000	25000000						3	0.073
2020-05-16T07:08:34	alpertron	laptop3	250000	25000000						3	0.073
2020-06-03T13:21:51	nordi	sweet16	250000	25000000						3	0.073
2020-06-19T03:40:34	nordi	sweet16	250000	25000000						3	0.073
2020-06-30T17:57:48	alan145	Bear	250000	25000000						3	0.073
2020-07-11T20:08:54	_p95holder_	TFL1_PRPt8pE_n	250000	25000000						3	0.073
2020-07-23T23:24:57	Ahmed Azhad	c5.4xlarge.azf	250000	25000000						3	0.073
2020-08-07T02:02:43	Ahmed Azhad	c5.xlarge.az	250000	25000000						3	0.073
2020-09-19T08:59:09	nordi	sweet16	250000	25000000						7	0.171
2020-10-25T08:18:09	nordi	sweet16	250000	25000000						7	0.171
2020-11-08T13:33:35	nordi	sweet16	250000	25000000						7	0.171
2021-01-05T07:06:13	_p95holder_	TFL17_PRPt12pE_k	250000	25000000						7	0.171
2021-01-29T05:15:26	mnd9	consult	250000	25000000						7	0.171
2021-03-08T22:46:40	_p95holder_	TFL1_PRPt8pE_n	250000	25000000						7	0.171
2021-04-26T22:07:30	nordi	sweet16	250000	38500000						7	0.201
2021-06-23T14:40:03	_p95holder_	TFL15_PRPt13pE_s	250000	25000000						7	0.171
2022-07-20T23:32:34	MarkS	desktop-i7	250000	31250000						7	0.185
2022-08-20T22:08:35	debrouxl	dl380g9-1	250000	36000000						7	0.195
2022-09-19T19:53:31	debrouxl	dl380g9-1	250000	36000000						7	0.195

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