M256181 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	10035812696910	5,417.9473	73.0257%	5,417.9473	73.0257%	73.0257%
PrimeNet	2⁴⁰	0.0000	55.0000%	2600	70000	0.0001	14.2551%	0.0001	61.4148%	6.4148%
GPU72	2⁴⁴	0.0000	59.0909%	4500	110000	0.0001	10.1985%	0.0001	63.2630%	4.1721%
Difference	-44	0.0000	-59.0909%	+29995500	+10035812586910	+5,417.9472	+62.8272%	+5,417.9472	+9.7627%	+9.7627%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

unknown

30000000

10035812696910

5,417.9473

73.0257%

5,417.9473

73.0257%

PrimeNet

2⁴⁰

0.0000

55.0000%

2600

70000

0.0001

14.2551%

0.0001

61.4148%

6.4148%

GPU72

2⁴⁴

0.0000

59.0909%

4500

110000

0.0001

10.1985%

0.0001

63.2630%

4.1721%

Difference

-44

0.0000

-59.0909%

+29995500

+10035812586910

+5,417.9472

+62.8272%

+5,417.9472

+9.7627%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
256181	19982119	8	24.252	39 3 × 13	-	3	13	8.798e-12	3.512e-8	6.050e-8
256181	92688573402819760348204129	26	86.261	180904464817491852144 2⁴ × 3² × 19 × 61 × 1083935293940489	2020-11-22	61	1083935293940489	119,486,808	585,144	1,092,887

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

256181

19982119

24.252

39
3 × 13

8.798e-12

3.512e-8

6.050e-8

256181

92688573402819760348204129

86.261

180904464817491852144
2⁴ × 3² × 19 × 61 × 1083935293940489

2020-11-22

1083935293940489

119,486,808

585,144

1,092,887

exponent	prime factors	composite factor	digits	bits*
256181	19982119 92688573402819760348204129	1852114103675379386829296341969351	34	110.513

exponent

prime factors

composite factor

digits

bits*

256181

19982119
92688573402819760348204129

1852114103675379386829296341969351

110.513

	GHz-Days	worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved
2021-09-05T19:58:20	Oliver Kruse	Ollaptop	30000000	3000000000	24	-	skipped known factor: 19982119	-	-	1.901	-	-	44.068%
2022-04-27T10:45:29	Oliver Kruse	Threadripper-PC	30000000	10035812696910		-	skipped known factor: 19982119	-	-	5,418	-	-	63.170%

GHz-Days

worth

Factor
probability

date

userid

compid

stage

factor

digits

bits*

spent

saved

2021-09-05T19:58:20

Oliver Kruse

Ollaptop

30000000

3000000000

skipped known factor: 19982119

1.901

-

-

44.068%

2022-04-27T10:45:29

Oliver Kruse

Threadripper-PC

30000000

10035812696910

skipped known factor: 19982119

5,418

-

-

63.170%

ECM factoring results:

Old Calculation Method

Total ECM effort:	11.362 GHz-days
Estimated T-Level:	26.945

Digits	B1	Curves	Complete	FacMiss
20	11000	530 / 100	5.300	0.486%
25	50000	530 / 280	1.893	15.013%
30	250000	249 / 640	0.389	67.749%

New Calculation Method

Total ECM effort:	11.362 GHz-days
Estimated T-Level:	26.945

Digits	B1	Complete	FacMiss
20	11000	29.815	0.000%
25	50000	3.857	2.114%
30	250000	0.379	68.478%
35	1000000	0.030	97.081%
40	3000000	0.002	99.809%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		281	2.048
250000	25000000		206	7.505
250000	25000000	92688573402819760348204129	1	0.036
250000	33000000		7	0.282
250000	34750000		7	0.288
250000	38250000		7	0.300
250000	38500000		21	0.902

ECM Details

										GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2014-09-05T15:14:00	TJAOI	Manual testing	50000	5000000						50	0.364
2015-01-02T14:31:00	TJAOI	Manual testing	50000	5000000						50	0.364
2015-09-18T09:51:00	TJAOI	Manual testing	50000	5000000						90	0.656
2016-02-26T13:29:03	TJAOI	Manual testing	50000	5000000						91	0.663
2017-06-16T16:31:55	TJAOI	Manual testing	250000	25000000						44	1.603
2020-01-06T15:15:45	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.109
2020-01-08T20:54:12	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.109
2020-01-11T00:06:15	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.109
2020-01-13T06:12:15	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.109
2020-01-15T10:30:23	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.109
2020-01-17T15:13:44	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.109
2020-01-19T23:56:00	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.109
2020-01-22T08:23:44	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.109
2020-01-24T14:56:38	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.109
2020-01-27T02:43:36	-Anonymous-	aws-nano	250000	25000000						3	0.109
2020-01-29T17:50:32	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.109
2020-02-01T16:30:16	-Anonymous-	aws-nano	250000	25000000						3	0.109
2020-02-04T16:09:19	kracker	O0	250000	25000000						3	0.109
2020-02-07T18:56:52	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.109
2020-02-11T06:07:38	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.109
2020-02-14T19:40:13	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.109
2020-04-22T04:01:58	_p95holder_	TFL15_PRPt13pE_s	250000	25000000						3	0.109
2020-04-23T05:18:57	kracker	O0	250000	25000000						3	0.109
2020-04-24T02:10:05	Oliver Kruse	IOS-2	250000	25000000						3	0.109
2020-04-24T15:48:17	Oliver Kruse	IOS-2	250000	25000000						3	0.109
2020-04-25T05:54:09	Oliver Kruse	IOS-1	250000	25000000						3	0.109
2020-04-26T04:29:52	Oliver Kruse	IOS-2	250000	25000000						3	0.109
2020-04-26T07:06:36	Bommer	3770K	250000	25000000						3	0.109
2020-04-26T16:43:10	Oliver Kruse	IOS-2	250000	25000000						3	0.109
2020-04-27T03:27:39	kracker	O0	250000	25000000						3	0.109
2020-04-27T10:08:14	Greg	azure	250000	25000000						3	0.109
2020-05-01T16:39:29	Greg	azure2	250000	25000000						3	0.109
2020-05-06T19:15:44	Greg Hogan	azure3	250000	25000000						3	0.109
2020-05-23T01:46:44	Oliver Kruse	IOS-3	250000	25000000						3	0.109
2020-06-08T02:59:18	_p95holder_	TFL18_PRPt12pE_m	250000	25000000						3	0.109
2020-06-15T09:53:04	TJAOI	Manual testing	250000	25000000						16	0.583
2020-10-02T06:37:27	nordi	sweet16	250000	25000000						7	0.255
2020-10-31T08:58:44	_p95holder_	TFL15_PRPt13pE_s	250000	25000000						7	0.255
2020-11-22T09:53:57	MarkS	desktop-i7	250000	25000000	92688573402819760348204129	86.261	1	2	1779696627644484	1	0.036
2020-11-27T10:14:07	nordi	sweet16	250000	25000000						7	0.255
2021-01-17T16:37:25	Chang Chia-Tche	exbpc13	250000	25000000						7	0.255
2021-02-11T18:24:51	_p95holder_	TFL1_PRPt8pE_n	250000	25000000						7	0.255
2021-04-04T18:39:41	Deufo	Ryzen2600	250000	38500000						7	0.301
2021-05-22T13:56:42	ZacHFX	5950X	250000	38500000						7	0.301
2021-07-17T22:08:30	Eric	miniPCWindows	250000	38250000						7	0.300
2021-08-22T18:20:28	Dylan Delgado	colab	250000	38500000						7	0.301
2021-10-01T09:24:12	MarkS	laptop64	250000	25000000						7	0.255
2021-11-08T09:07:35	mnd9	f4	250000	25000000						7	0.255
2022-01-24T04:33:23	Massimo Cappelli (ik5pwa)	maxlinux_8	250000	25000000						7	0.255
2022-03-20T11:21:22	Alex Kruppa	lily	250000	34750000						7	0.288
2022-05-17T02:49:58	Dylan Delgado	laptop-ryzen73700	250000	33000000						7	0.282

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