M251809 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	unknown	30000000	10120247026890	4,486.3114	73.0065%	4,486.3114	73.0065%	73.0065%
PrimeNet	2⁴⁰	0.0000	55.0000%	2600	70000	0.0001	14.2202%	0.0001	61.3991%	6.3991%
GPU72	2⁴⁴	0.0000	59.0909%	4500	110000	0.0001	10.1715%	0.0001	63.2520%	4.1611%
Difference	-44	0.0000	-59.0909%	+29995500	+10120246916890	+4,486.3113	+62.8350%	+4,486.3113	+9.7545%	+9.7545%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

unknown

30000000

10120247026890

4,486.3114

73.0065%

4,486.3114

73.0065%

PrimeNet

2⁴⁰

0.0000

55.0000%

2600

70000

0.0001

14.2202%

0.0001

61.3991%

6.3991%

GPU72

2⁴⁴

0.0000

59.0909%

4500

110000

0.0001

10.1715%

0.0001

63.2520%

4.1611%

Difference

-44

0.0000

-59.0909%

+29995500

+10120246916890

+4,486.3113

+62.8350%

+4,486.3113

+9.7545%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
251809	249290911	9	27.893	495 3² × 5 × 11	-	9	11	7.862e-11	7.411e-8	1.490e-7
251809	1504702637095119054728409047	28	90.282	2987785657174920385547 739 × 220223981 × 18358635133	2021-08-31	220223981	18358635133	1.808e+9	9.832	15.199

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

251809

249290911

27.893

495
3² × 5 × 11

7.862e-11

7.411e-8

1.490e-7

251809

1504702637095119054728409047

90.282

2987785657174920385547
739 × 220223981 × 18358635133

2021-08-31

220223981

18358635133

1.808e+9

9.832

15.199

exponent	prime factors	composite factor	digits	bits*
251809	249290911 1504702637095119054728409047	375108691185544622806703948907271817	36	118.175

exponent

prime factors

composite factor

digits

bits*

251809

249290911
1504702637095119054728409047

375108691185544622806703948907271817

118.175

	GHz-Days	worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved
2021-06-01T16:43:33	ViliamF	3	50000000	7150000000		-	skipped known factor: 249290911	-	-	3.554	-	-	46.553%
2021-08-21T11:51:06	Oliver Kruse	Ollaptop	30000000	3000000000	24	-	skipped known factor: 249290911	-	-	1.561	-	-	44.033%
2022-04-21T09:21:37	Oliver Kruse	Threadripper-PC	30000000	10120247026890		-	skipped known factor: 249290911	-	-	4,486	-	-	63.147%

GHz-Days

worth

Factor
probability

date

userid

compid

stage

factor

digits

bits*

spent

saved

2021-06-01T16:43:33

ViliamF

50000000

7150000000

skipped known factor: 249290911

3.554

-

-

46.553%

2021-08-21T11:51:06

Oliver Kruse

Ollaptop

30000000

3000000000

skipped known factor: 249290911

1.561

-

-

44.033%

2022-04-21T09:21:37

Oliver Kruse

Threadripper-PC

30000000

10120247026890

skipped known factor: 249290911

4,486

-

-

63.147%

ECM factoring results:

Old Calculation Method

Total ECM effort:	15.924 GHz-days
Estimated T-Level:	27.664

Digits	B1	Curves	Complete	FacMiss
20	11000	622 / 100	6.220	0.193%
25	50000	622 / 280	2.221	10.802%
30	250000	341 / 640	0.533	58.671%

New Calculation Method

Total ECM effort:	15.924 GHz-days
Estimated T-Level:	27.664

Digits	B1	Complete	FacMiss
20	11000	38.239	0.000%
25	50000	5.123	0.596%
30	250000	0.518	59.554%
35	1000000	0.041	95.946%
40	3000000	0.003	99.729%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		281	1.680
250000	25000000		222	6.638
250000	25000000	1504702637095119054728409047	5	0.149
250000	37904147		7	0.245
250000	38500000		7	0.247
250000	125000000		100	6.965

ECM Details

										GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2014-08-22T10:14:00	TJAOI	Manual testing	50000	5000000						50	0.299
2015-01-02T14:31:00	TJAOI	Manual testing	50000	5000000						50	0.299
2015-10-02T10:43:37	TJAOI	Manual testing	50000	5000000						90	0.538
2016-03-04T13:11:40	TJAOI	Manual testing	50000	5000000						91	0.544
2017-08-11T11:12:16	TJAOI	Manual testing	250000	25000000						44	1.316
2019-12-29T13:56:33	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.090
2019-12-31T12:27:51	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.090
2020-01-02T12:48:23	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.090
2020-01-04T17:29:47	kracker	O0	250000	25000000						3	0.090
2020-01-06T18:56:49	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.090
2020-01-09T00:33:48	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.090
2020-01-11T05:14:39	kracker	O0	250000	25000000						3	0.090
2020-01-13T09:58:46	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.090
2020-01-15T13:50:06	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.090
2020-01-17T19:07:43	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.090
2020-01-20T04:42:40	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.090
2020-01-22T12:13:13	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.090
2020-01-24T18:50:17	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.090
2020-01-27T08:12:25	kracker	O0	250000	25000000						3	0.090
2020-01-29T22:17:07	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.090
2020-02-01T17:38:26	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.090
2020-02-04T21:17:13	-Anonymous-	aws-nano	250000	25000000						3	0.090
2020-02-08T01:17:22	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.090
2020-02-11T11:02:18	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.090
2020-02-15T02:45:42	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.090
2020-02-18T08:02:29	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.090
2020-02-21T18:40:17	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.090
2020-02-25T15:31:19	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.090
2020-03-02T11:00:37	_p95holder_	TFL18_PRPt12pE_m	250000	25000000						3	0.090
2020-03-04T08:58:10	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.090
2020-03-09T13:48:36	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.090
2020-03-15T11:36:56	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.090
2020-03-20T22:01:47	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.090
2020-03-23T10:24:18	TJAOI	Manual testing	250000	25000000						73	2.183
2021-04-23T05:36:53	_p95holder_	TFL18_PRPt12pE_m	250000	25000000						7	0.209
2021-06-08T01:13:37	_p95holder_	TFL17_PRPt12pE_k	250000	25000000						7	0.209
2021-07-24T00:47:06	Eric	miniPCWindows	250000	38500000						7	0.247
2021-08-31T01:25:01	MarkS	desktop-i7	250000	25000000	1504702637095119054728409047	90.282	5	2	7720807881802678	5	0.149
2021-09-23T17:45:36	Ahmed Azhad	c5.azf2	250000	37904147						7	0.245
2021-11-07T00:25:24	mnd9	f4	250000	25000000						7	0.209
2022-01-23T05:55:03	Oliver Kruse	11700K	250000	125000000						100	6.965

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