M258421 Mersenne number exponent details

Residue

Status

L-L

6271683FFC4B1D2D

double-checked

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	114.9826	73.1343%	30000000	10035812696910	5,417.9473	23.4493%	5,532.9299	79.4341%	6.2998%
PrimeNet	2⁴⁰	0.0000	55.0000%	2600	70000	0.0001	14.2727%	0.0001	61.4227%	6.4227%
GPU72	2⁴⁴	0.0000	59.0909%	4500	120000	0.0001	10.3918%	0.0001	63.3421%	4.2512%
Difference	+23	+114.9826	+14.0434%	+29995500	+10035812576910	+5,417.9472	+13.0575%	+5,532.9298	+16.0920%	+16.0920%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

114.9826

73.1343%

30000000

10035812696910

5,417.9473

23.4493%

5,532.9299

79.4341%

6.2998%

PrimeNet

2⁴⁰

0.0000

55.0000%

2600

70000

0.0001

14.2727%

0.0001

61.4227%

6.4227%

GPU72

2⁴⁴

0.0000

59.0909%

4500

120000

0.0001

10.3918%

0.0001

63.3421%

4.2512%

Difference

+23

+114.9826

+14.0434%

+29995500

+10035812576910

+5,417.9472

+13.0575%

+5,532.9298

+16.0920%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
258421	152240511081040601215640857	27	86.976	294559093651523291868 2² × 3 × 269 × 9229751 × 9886644631	2020-09-30	9229751	9886644631	107,740,090	5.4236	9.968
258421	411000250694020448155701439	27	88.409	795214496294845326339 3 × 265071498764948442113	2009-04-20	3	265071498764948442113	304,476,016	1.431e+11	2.673e+11
258421	1668811974756299277537204839	28	90.431	3228862930559628044039 7 × 37 × 743 × 16778805170313547	2017-06-02	743	16778805170313547	1.789e+9	9,057,758	16,917,370

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

258421

152240511081040601215640857

86.976

294559093651523291868
2² × 3 × 269 × 9229751 × 9886644631

2020-09-30

9229751

9886644631

107,740,090

5.4236

9.968

258421

411000250694020448155701439

88.409

795214496294845326339
3 × 265071498764948442113

2009-04-20

265071498764948442113

304,476,016

1.431e+11

2.673e+11

258421

1668811974756299277537204839

90.431

3228862930559628044039
7 × 37 × 743 × 16778805170313547

2017-06-02

743

16778805170313547

1.789e+9

9,057,758

16,917,370

exponent	prime factors	composite factor	digits	bits*
258421	152240511081040601215640857 411000250694020448155701439	62570888220093485087695525148496129408944366742093 223	53	175.386
258421	152240511081040601215640857 1668811974756299277537204839	25406078793505962823130625259682435136927193986650 7023	54	177.407
258421	411000250694020448155701439 1668811974756299277537204839	68588213998602232675057851443864446085775104147006 3321	54	178.840
258421	152240511081040601215640857 411000250694020448155701439 1668811974756299277537204839	10441904753282987286945463601062519333772721769675 3916558175275717142915384706097	81	265.817

exponent

prime factors

composite factor

digits

bits*

258421

152240511081040601215640857
411000250694020448155701439

62570888220093485087695525148496129408944366742093
223

175.386

258421

152240511081040601215640857
1668811974756299277537204839

25406078793505962823130625259682435136927193986650
7023

177.407

258421

411000250694020448155701439
1668811974756299277537204839

68588213998602232675057851443864446085775104147006
3321

178.840

258421

152240511081040601215640857
411000250694020448155701439
1668811974756299277537204839

10441904753282987286945463601062519333772721769675
3916558175275717142915384706097

265.817

	GHz-Days	worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved
2000-12-31T00:00:00	ANONYMOUS	v4_computers	95000	3800000		-		-	-	0.003	-	-	2.203%
2001-06-17T00:00:00	ANONYMOUS	v4_computers	100000	10000000		-		-	-	0.006	-	-	2.725%
2002-06-02T00:00:00	ANONYMOUS	v4_computers	32768	3276800		-		-	-	0.002	-	-	1.562%
2002-08-10T00:00:00	ANONYMOUS	v4_computers	65536	6553600		-		-	-	0.004	-	-	2.245%
2003-03-07T00:00:00	ANONYMOUS	v4_computers	131072	13107200		-		-	-	0.008	-	-	3.057%
2003-11-08T00:00:00	ANONYMOUS	v4_computers	262144	26214400		-		-	-	0.017	-	-	3.984%
2021-08-25T14:39:23	Oliver Kruse	Ollaptop	30000000	3000000000	24	-		-	-	1.901	-	-	12.599%
2022-04-30T06:31:25	Oliver Kruse	Threadripper-PC	30000000	10035812696910		-	skipped known factor: 152240511081040601215640857	-	-	5,418	-	-	23.449%

GHz-Days

worth

Factor
probability

date

userid

compid

stage

factor

digits

bits*

spent

saved

2000-12-31T00:00:00

ANONYMOUS

v4_computers

95000

3800000

0.003

-

-

2.203%

2001-06-17T00:00:00

ANONYMOUS

v4_computers

100000

10000000

0.006

-

-

2.725%

2002-06-02T00:00:00

ANONYMOUS

v4_computers

32768

3276800

0.002

-

-

1.562%

2002-08-10T00:00:00

ANONYMOUS

v4_computers

65536

6553600

0.004

-

-

2.245%

2003-03-07T00:00:00

ANONYMOUS

v4_computers

131072

13107200

0.008

-

-

3.057%

2003-11-08T00:00:00

ANONYMOUS

v4_computers

262144

26214400

0.017

-

-

3.984%

2021-08-25T14:39:23

Oliver Kruse

Ollaptop

30000000

3000000000

1.901

-

-

12.599%

2022-04-30T06:31:25

Oliver Kruse

Threadripper-PC

30000000

10035812696910

skipped known factor: 152240511081040601215640857

5,418

-

-

23.449%

	Bits	Factor	GHz-Days	worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved
1999-11-24T00:00:00	ANONYMOUS	v4_computers	2⁵²	2⁵³		-	-	0.002	-	-
2000-04-27T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁴		-	-	0.009	-	-
2000-12-31T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁵		-	-	0.019	-	-
2001-02-18T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁶		-	-	0.037	-	-
2002-03-24T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁷		-	-	0.074	-	-
2022-03-07T05:52:30	LordJulius	Manual testing	2⁵⁷	2⁵⁸		-	-	0.074	-	-
2009-01-01T21:04:00	Sturle Sunde	gorro.ifi	2⁵⁸	2⁵⁹		-	-	0.149	-	-
2009-01-25T12:25:00	Sturle Sunde	gooch.ifi	2⁵⁹	2⁶⁰		-	-	0.297	-	-

Bits

Factor

GHz-Days

worth

date

userid

compid

from

factor

bits*

digits

spent

saved

1999-11-24T00:00:00

ANONYMOUS

v4_computers

2⁵²

2⁵³

0.002

-

-

2000-04-27T00:00:00

ANONYMOUS

v4_computers

2¹

2⁵⁴

0.009

-

-

2000-12-31T00:00:00

ANONYMOUS

v4_computers

2¹

2⁵⁵

0.019

-

-

2001-02-18T00:00:00

ANONYMOUS

v4_computers

2¹

2⁵⁶

0.037

-

-

2002-03-24T00:00:00

ANONYMOUS

v4_computers

2¹

2⁵⁷

0.074

-

-

2022-03-07T05:52:30

LordJulius

Manual testing

2⁵⁷

2⁵⁸

0.074

-

-

2009-01-01T21:04:00

Sturle Sunde

gorro.ifi

2⁵⁸

2⁵⁹

0.149

-

-

2009-01-25T12:25:00

Sturle Sunde

gooch.ifi

2⁵⁹

2⁶⁰

0.297

-

-

ECM factoring results:

Old Calculation Method

Total ECM effort:	10.407 GHz-days
Estimated T-Level:	26.906

Digits	B1	Curves	Complete	FacMiss
20	11000	433 / 100	4.330	1.288%
25	50000	433 / 280	1.546	21.242%
30	250000	244 / 640	0.381	68.280%

New Calculation Method

Total ECM effort:	10.407 GHz-days
Estimated T-Level:	26.906

Digits	B1	Complete	FacMiss
20	11000	26.430	0.000%
25	50000	3.514	2.978%
30	250000	0.354	70.193%
35	1000000	0.028	97.220%
40	3000000	0.002	99.816%

ECM Summary

B1	B2	factor	curves	GHz-days
		411000250694020448155701439	1	0.00000e+0
50000	5000000		189	1.378
250000	25000000		210	7.653
250000	25000000	152240511081040601215640857	2	0.073
250000	25000000	1668811974756299277537204839	11	0.401
250000	38500000		21	0.903

ECM Details

										GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2007-08-09T13:21:00	George Woltman	D_P4Debug	50000	5000000						1	0.007
2007-08-17T15:55:00	ANONYMOUS	Bayes	50000	5000000						1	0.007
2007-08-29T14:10:00	Chad Davis	Bayes	50000	5000000						1	0.007
2007-09-11T16:45:00	Chad Davis	Bayes	50000	5000000						1	0.007
2007-10-10T08:28:00	ANONYMOUS	minister	50000	5000000						1	0.007
2007-12-29T02:31:00	Chad Davis	Bayes	50000	5000000						1	0.007
2007-12-29T04:13:00	Chad Davis	Bayes	50000	5000000						1	0.007
2007-12-29T04:56:00	Steve Scott	Abit	50000	5000000						1	0.007
2007-12-29T08:30:00	James Heinrich	WHS	50000	5000000						1	0.007
2007-12-29T19:08:00	Steve Scott	Celeron	50000	5000000						1	0.007
2007-12-30T09:00:00	Chad Davis	Bayes	50000	5000000						1	0.007
2008-02-10T12:18:00	Steve Scott	Abit-2	50000	5000000						3	0.022
2008-08-18T15:51:00	Sturle Sunde	v22	50000	5000000						3	0.022
2008-09-18T14:33:00	Sturle Sunde	v21	50000	5000000						3	0.022
2008-10-17T15:42:00	Sturle Sunde	v22	50000	5000000						3	0.022
2008-11-18T07:01:00	Jayson King	atlas	50000	5000000						3	0.022
2008-12-08T14:47:00	Jayson King	atlas	50000	5000000						3	0.022
2009-01-15T17:16:00	Sturle Sunde	v21	50000	5000000						3	0.022
2009-02-14T23:54:00	Sturle Sunde	v22	50000	5000000						3	0.022
2009-03-04T19:59:00	ANONYMOUS	v23	50000	5000000						3	0.022
2009-03-21T06:21:00	Sturle Sunde	v22	50000	5000000						3	0.022
2009-04-09T12:34:00	Lupo	yorick	50000	5000000						3	0.022
2009-04-16T02:26:00	Sturle Sunde	v23	50000	5000000						3	0.022
2009-04-20T15:02:00	Sturle Sunde	v23			411000250694020448155701439	88.409		1		1	-
2014-09-19T12:42:00	TJAOI	Manual testing	50000	5000000						2	0.015
2015-01-23T13:28:00	TJAOI	Manual testing	50000	5000000						50	0.364
2015-09-18T09:51:00	TJAOI	Manual testing	50000	5000000						90	0.656
2017-06-02T16:26:19	TJAOI	Manual testing	250000	25000000						33	1.203
2017-06-02T16:26:19	TJAOI	Manual testing	250000	25000000	1668811974756299277537204839	90.431	11	2		11	0.401
2020-01-10T20:03:58	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.109
2020-01-13T03:12:52	kracker	O0	250000	25000000						3	0.109
2020-01-15T06:36:35	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.109
2020-01-17T11:12:08	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.109
2020-01-19T21:06:21	kracker	O0	250000	25000000						3	0.109
2020-01-22T04:07:35	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.109
2020-01-24T11:10:32	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.109
2020-01-26T23:06:46	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.109
2020-01-29T12:47:44	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.109
2020-02-01T07:36:08	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.109
2020-02-04T08:38:48	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.109
2020-02-07T14:34:10	kracker	O0	250000	25000000						3	0.109
2020-02-10T22:27:53	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.109
2020-02-14T13:01:18	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.109
2020-07-06T08:19:10	TJAOI	Manual testing	250000	25000000						58	2.114
2020-09-30T15:51:06	nordi	sweet16	250000	25000000	152240511081040601215640857	86.976	2	2	224623413969443	2	0.073
2020-11-07T02:37:49	Tsurumaki Kokoro	Baidu_HK_1	250000	25000000						7	0.255
2020-11-07T05:05:07	_p95holder_	TFL18_PRPt12pE_m	250000	25000000						7	0.255
2020-11-28T21:09:44	_p95holder_	TFL15_PRPt13pE_s	250000	25000000						7	0.255
2021-01-19T00:19:14	Chang Chia-Tche	exbpc13	250000	25000000						7	0.255
2021-02-14T08:19:17	mnd9	consult	250000	25000000						7	0.255
2021-04-10T18:36:21	_p95holder_	TFL15_PRPt13pE_s	250000	25000000						7	0.255
2021-05-31T16:04:22	MarkS	desktop-i7	250000	25000000						7	0.255
2021-07-13T07:59:53	_p95holder_	TFL18_PRPt12pE_m	250000	25000000						7	0.255
2021-08-13T05:34:54	Dylan Delgado	colab	250000	38500000						7	0.301
2021-09-22T20:33:00	Ahmed Azhad	c5.4xlarge.azf	250000	38500000						7	0.301
2021-11-06T05:14:37	mnd9	f4	250000	25000000						7	0.255
2022-01-15T00:21:04	Dylan Delgado	colab	250000	38500000						7	0.301
2022-03-19T15:37:35	_p95holder_	TFL15_PRPt13pE_s	250000	25000000						7	0.255
2022-05-15T16:11:30	Corey	tab	250000	25000000						7	0.255

date	userid	compid	res64	spent (GHz-days)
2001-10-13T00:00:00	ANONYMOUS	v4_computers	6271683FFC4B1D2D	0.002

date

userid

compid

res64

spent (GHz-days)

2001-10-13T00:00:00

ANONYMOUS

v4_computers

6271683FFC4B1D2D

0.002

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 = 30000000, B2 = 10035812696910 (P-1 stage 2)

B1 = 30000000, B2 = 3000000000 (P-1 stage 2)

B1 = 30000000 (P-1 stage 1)

B1 = 262144, B2 = 26214400 (P-1 stage 2)

B1 = 131072, B2 = 13107200 (P-1 stage 2)

B1 = 100000, B2 = 10000000 (P-1 stage 2)

B1 = 65536, B2 = 6553600 (P-1 stage 2)

B1 = 95000, B2 = 3800000 (P-1 stage 2)

B1 = 262144 (P-1 stage 1)

B1 = 32768, B2 = 3276800 (P-1 stage 2)

B1 = 131072 (P-1 stage 1)

B1 = 100000 (P-1 stage 1)

B1 = 95000 (P-1 stage 1)

B1 = 65536 (P-1 stage 1)

B1 = 32768 (P-1 stage 1)

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

10¹²

10¹³

10¹⁴

10¹⁵

10¹⁶

10¹⁷

10¹⁸

10¹⁹

10²⁰

10²¹

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