M241727 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	122.9235	73.1343%	30000000	10120247026890	4,486.3114	23.3740%	4,609.2349	79.4139%	6.2796%
PrimeNet	2⁴⁰	0.0000	55.0000%	2600	65000	0.0000	13.9475%	0.0000	61.2764%	6.2764%
GPU72	2⁴⁴	0.0000	59.0909%	4500	110000	0.0001	10.1076%	0.0001	63.2258%	4.1349%
Difference	+23	+122.9234	+14.0434%	+29995500	+10120246916890	+4,486.3113	+13.2664%	+4,609.2348	+16.1881%	+16.1881%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

122.9235

73.1343%

30000000

10120247026890

4,486.3114

23.3740%

4,609.2349

79.4139%

6.2796%

PrimeNet

2⁴⁰

0.0000

55.0000%

2600

65000

0.0000

13.9475%

0.0000

61.2764%

6.2764%

GPU72

2⁴⁴

0.0000

59.0909%

4500

110000

0.0001

10.1076%

0.0001

63.2258%

4.1349%

Difference

+23

+122.9234

+14.0434%

+29995500

+10120246916890

+4,486.3113

+13.2664%

+4,609.2348

+16.1881%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
241727	191518345935288787913	21	67.376	396145953772828 2² × 7 × 139 × 101784674659	2008-01-10	139	101784674659	123.67	45.119	84.270
241727	3253841460776382539818669866719	31	101.360	6730405500371043656312017 13 × 79 × 811 × 8080717664214234961	2020-11-09	811	8080717664214234961	6.608e+11	3.582e+9	6.690e+9

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

241727

191518345935288787913

67.376

396145953772828
2² × 7 × 139 × 101784674659

2008-01-10

139

101784674659

123.67

45.119

84.270

241727

3253841460776382539818669866719

101.360

6730405500371043656312017
13 × 79 × 811 × 8080717664214234961

2020-11-09

811

8080717664214234961

6.608e+11

3.582e+9

6.690e+9

exponent	prime factors	composite factor	digits	bits*
241727	191518345935288787913 3253841460776382539818669866719	62317033450355663502357641057921365850651076816744 7	51	168.736

exponent

prime factors

composite factor

digits

bits*

241727

191518345935288787913
3253841460776382539818669866719

62317033450355663502357641057921365850651076816744
7

168.736

	GHz-Days	worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved
2000-11-05T00:00:00	ANONYMOUS	v4_computers	100000	4000000		-		-	-	0.003	-	-	2.232%
2001-06-03T00:00:00	ANONYMOUS	v4_computers	100000	10000000		-		-	-	0.005	-	-	2.698%
2002-06-02T00:00:00	ANONYMOUS	v4_computers	32768	3276800		-		-	-	0.002	-	-	1.543%
2002-08-03T00:00:00	ANONYMOUS	v4_computers	65536	6553600		-		-	-	0.003	-	-	2.221%
2003-03-07T00:00:00	ANONYMOUS	v4_computers	131072	13107200		-		-	-	0.007	-	-	3.027%
2003-10-31T00:00:00	ANONYMOUS	v4_computers	262144	26214400		-		-	-	0.014	-	-	3.950%
2021-08-06T06:44:39	Oliver Kruse	Ollaptop	30000000	3000000000	24	-		-	-	1.561	-	-	12.536%
2022-04-08T11:52:10	Oliver Kruse	Threadripper-PC	30000000	10120247026890		-	skipped known factor: 191518345935288787913	-	-	4,486	-	-	23.374%

GHz-Days

worth

Factor
probability

date

userid

compid

stage

factor

digits

bits*

spent

saved

2000-11-05T00:00:00

ANONYMOUS

v4_computers

100000

4000000

0.003

-

-

2.232%

2001-06-03T00:00:00

ANONYMOUS

v4_computers

100000

10000000

0.005

-

-

2.698%

2002-06-02T00:00:00

ANONYMOUS

v4_computers

32768

3276800

0.002

-

-

1.543%

2002-08-03T00:00:00

ANONYMOUS

v4_computers

65536

6553600

0.003

-

-

2.221%

2003-03-07T00:00:00

ANONYMOUS

v4_computers

131072

13107200

0.007

-

-

3.027%

2003-10-31T00:00:00

ANONYMOUS

v4_computers

262144

26214400

0.014

-

-

3.950%

2021-08-06T06:44:39

Oliver Kruse

Ollaptop

30000000

3000000000

1.561

-

-

12.536%

2022-04-08T11:52:10

Oliver Kruse

Threadripper-PC

30000000

10120247026890

skipped known factor: 191518345935288787913

4,486

-

-

23.374%

	Bits	Factor	GHz-Days	worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved
1999-11-17T00:00:00	ANONYMOUS	v4_computers	2⁵²	2⁵³		-	-	0.002	-	-
2000-04-19T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁴		-	-	0.010	-	-
2022-03-07T05:44:55	LordJulius	Manual testing	2⁵⁴	2⁵⁵		-	-	0.010	-	-
2001-02-18T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁶		-	-	0.040	-	-
2002-04-07T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁷		-	-	0.079	-	-

Bits

Factor

GHz-Days

worth

date

userid

compid

from

factor

bits*

digits

spent

saved

1999-11-17T00:00:00

ANONYMOUS

v4_computers

2⁵²

2⁵³

0.002

-

-

2000-04-19T00:00:00

ANONYMOUS

v4_computers

2¹

2⁵⁴

0.010

-

-

2022-03-07T05:44:55

LordJulius

Manual testing

2⁵⁴

2⁵⁵

0.010

-

-

2001-02-18T00:00:00

ANONYMOUS

v4_computers

2¹

2⁵⁶

0.040

-

-

2002-04-07T00:00:00

ANONYMOUS

v4_computers

2¹

2⁵⁷

0.079

-

-

ECM factoring results:

Old Calculation Method

Total ECM effort:	21.132 GHz-days
Estimated T-Level:	29.602

Digits	B1	Curves	Complete	FacMiss
20	11000	869 / 100	8.690	0.016%
25	50000	869 / 280	3.104	4.464%
30	250000	589 / 640	0.920	39.811%

New Calculation Method

Total ECM effort:	21.132 GHz-days
Estimated T-Level:	29.602

Digits	B1	Complete	FacMiss
20	11000	58.116	0.000%
25	50000	8.301	0.025%
30	250000	0.861	42.271%
35	1000000	0.070	93.233%
40	3000000	0.005	99.537%

ECM Summary

B1	B2	factor	curves	GHz-days
		191518345935288787913	1	0.00000e+0
50000	5000000		280	1.672
250000	25000000		237	7.077
250000	25000000	3253841460776382539818669866719	2	0.060
250000	38500000		350	12.32

ECM Details

										GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2007-08-05T05:23:00	George Woltman	D_P4Debug	50000	5000000						1	0.006
2007-08-16T16:46:00	ANONYMOUS	Bayes	50000	5000000						1	0.006
2007-08-27T12:44:00	Chad Davis	Bayes	50000	5000000						1	0.006
2007-09-07T01:12:00	Chad Davis	Bayes	50000	5000000						1	0.006
2007-09-30T14:23:00	Chad Davis	Bayes	50000	5000000						1	0.006
2007-11-16T19:55:00	ANONYMOUS	minister	50000	5000000						1	0.006
2008-01-10T07:41:00	Steve Scott	Abit-3			191518345935288787913	67.376		1		1	-
2014-08-15T10:40:00	TJAOI	Manual testing	50000	5000000						43	0.257
2015-01-09T16:37:00	TJAOI	Manual testing	50000	5000000						50	0.299
2015-09-04T10:44:00	TJAOI	Manual testing	50000	5000000						90	0.537
2016-05-13T16:16:34	TJAOI	Manual testing	50000	5000000						91	0.543
2017-06-09T13:18:37	TJAOI	Manual testing	250000	25000000						44	1.314
2019-12-16T04:10:26	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.090
2019-12-17T06:56:46	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.090
2019-12-18T11:14:36	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.090
2019-12-19T16:14:36	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.090
2019-12-21T04:12:52	Ducho_YYZ	oracleAU2	250000	25000000						3	0.090
2019-12-22T06:36:41	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.090
2019-12-23T15:12:27	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.090
2019-12-25T01:32:10	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.090
2019-12-27T00:58:05	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.090
2019-12-28T22:47:44	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.090
2019-12-30T20:48:21	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.090
2020-01-02T01:55:28	Chang Chia-Tche	exbpc13	250000	25000000						3	0.090
2020-01-03T23:50:11	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.090
2020-01-06T01:48:40	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.090
2020-01-08T07:16:20	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.090
2020-01-10T10:36:51	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.090
2020-01-12T16:18:29	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.090
2020-01-14T20:51:10	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.090
2020-01-17T01:22:56	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.090
2020-01-19T10:35:41	kracker	O0	250000	25000000						3	0.090
2020-01-21T17:59:41	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.090
2020-01-24T01:21:44	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.090
2020-01-26T11:30:53	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.090
2020-01-29T01:15:00	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.090
2020-01-31T20:37:07	-Anonymous-	aws-nano	250000	25000000						3	0.090
2020-02-03T19:40:34	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.090
2020-02-07T03:40:25	Adam B	dell	250000	25000000						3	0.090
2020-02-10T07:30:47	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.090
2020-02-13T22:32:19	kracker	O0	250000	25000000						3	0.090
2020-02-17T18:02:10	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.090
2020-02-20T23:03:40	kracker	O0	250000	25000000						3	0.090
2020-02-24T17:52:10	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.090
2020-02-27T19:23:17	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.090
2020-03-02T22:07:10	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.090
2020-03-07T15:59:56	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.090
2020-03-13T15:40:25	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.090
2020-03-19T23:54:49	astraeus	x7	250000	25000000						3	0.090
2020-04-02T06:16:14	Hans Loeblich	crow	250000	25000000						3	0.090
2020-04-16T23:18:42	Oliver Kruse	IOS-1	250000	25000000						3	0.090
2020-04-30T16:53:19	Greg	azure3	250000	25000000						3	0.090
2020-05-05T00:35:46	Greg Hogan	azure2	250000	25000000						3	0.090
2020-05-16T12:35:45	volki	home	250000	25000000						3	0.090
2020-06-03T20:47:03	_p95holder_	TFL17_PRPt12pE_k	250000	25000000						3	0.090
2020-06-19T09:10:40	Chang Chia-Tche	exbpc13	250000	25000000						3	0.090
2020-06-28T08:40:06	nordi	sweet16	250000	25000000						3	0.090
2020-07-12T06:18:42	MarkS	desktop-i7	250000	25000000						3	0.090
2020-07-24T00:31:45	Ahmed Azhad	c5.4xlarge.azf	250000	25000000						3	0.090
2020-08-07T20:34:31	Chang Chia-Tche	exbpc13	250000	25000000						3	0.090
2020-09-19T23:25:39	nordi	sweet16	250000	25000000						7	0.209
2020-10-25T19:37:42	MarkS	laptop64	250000	25000000						7	0.209
2020-11-09T05:24:39	nordi	sweet16	250000	25000000	3253841460776382539818669866719	101.360	2	2	5145202326750457	2	0.060
2020-11-23T19:22:08	nordi	sweet16	250000	25000000						7	0.209
2021-01-15T11:09:12	ZacHFX	Ryzen	250000	25000000						7	0.209
2021-02-09T21:29:24	chauvet_p		250000	25000000						7	0.209
2021-05-15T07:27:54	_p95holder_	TFL18_PRPt12pE_m	250000	25000000						7	0.209
2021-07-08T00:08:17	Ahmed Azhad	c5.4xlarge.azf2	250000	38500000						350	12.32
2021-10-14T23:03:42	mnd9	f4	250000	25000000						7	0.209

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