M256579 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	73.0290%	5,417.9473	73.0290%	73.0290%
PrimeNet	2⁴⁰	0.0000	55.0000%	2600	70000	0.0001	14.2582%	0.0001	61.4162%	6.4162%
GPU72	2⁴⁴	0.0000	59.0909%	4500	110000	0.0001	10.2010%	0.0001	63.2640%	4.1731%
Difference	-44	0.0000	-59.0909%	+29995500	+10035812586910	+5,417.9472	+62.8280%	+5,417.9472	+9.7650%	+9.7650%

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

73.0290%

5,417.9473

73.0290%

PrimeNet

2⁴⁰

0.0000

55.0000%

2600

70000

0.0001

14.2582%

0.0001

61.4162%

6.4162%

GPU72

2⁴⁴

0.0000

59.0909%

4500

110000

0.0001

10.2010%

0.0001

63.2640%

4.1731%

Difference

-44

0.0000

-59.0909%

+29995500

+10035812586910

+5,417.9472

+62.8280%

+5,417.9472

+9.7650%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
256579	7364843617	10	32.778	14352 2⁴ × 3 × 13 × 23	-	16	23	2.467e-9	1.623e-7	3.226e-7
256579	2059086847566011497673	22	70.802	4012578674727884 2² × 5897 × 39019 × 4359697	2016-03-11	39019	4359697	1,279.1	0.0027	0.0044
256579	216797667997308422734706119	27	87.486	422477420204514833121 3 × 1231 × 114399518062419397	2022-05-14	1231	114399518062419397	149,682,088	61,756,673	115,344,267

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

256579

7364843617

32.778

14352
2⁴ × 3 × 13 × 23

2.467e-9

1.623e-7

3.226e-7

256579

2059086847566011497673

70.802

4012578674727884
2² × 5897 × 39019 × 4359697

2016-03-11

39019

4359697

1,279.1

0.0027

0.0044

256579

216797667997308422734706119

87.486

422477420204514833121
3 × 1231 × 114399518062419397

2022-05-14

1231

114399518062419397

149,682,088

61,756,673

115,344,267

exponent	prime factors	composite factor	digits	bits*
256579	7364843617 2059086847566011497673	15164852626145191764785604403241	32	103.581
256579	7364843617 216797667997308422734706119	1596680921330462110358038044887992423	37	120.264
256579	2059086847566011497673 216797667997308422734706119	446405226756240577410519502928285205770707361087	48	158.289
256579	7364843617 2059086847566011497673 216797667997308422734706119	32877046848711360314582589497953941064759256738765 06131679	58	191.067

exponent

prime factors

composite factor

digits

bits*

256579

7364843617
2059086847566011497673

15164852626145191764785604403241

103.581

256579

7364843617
216797667997308422734706119

1596680921330462110358038044887992423

120.264

256579

2059086847566011497673
216797667997308422734706119

446405226756240577410519502928285205770707361087

158.289

256579

7364843617
2059086847566011497673
216797667997308422734706119

32877046848711360314582589497953941064759256738765
06131679

191.067

	GHz-Days	worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved
2021-09-08T17:08:00	Oliver Kruse	Ollaptop	30000000	3000000000	24	-	skipped known factor: 7364843617 skipped known factor: 2059086847566011497673	-	-	1.901	-	-	44.071%
2022-04-27T23:27:09	Oliver Kruse	Threadripper-PC	30000000	10035812696910		-	skipped known factor: 7364843617 skipped known factor: 2059086847566011497673	-	-	5,418	-	-	63.174%

GHz-Days

worth

Factor
probability

date

userid

compid

stage

factor

digits

bits*

spent

saved

2021-09-08T17:08:00

Oliver Kruse

Ollaptop

30000000

3000000000

skipped known factor: 7364843617
skipped known factor: 2059086847566011497673

1.901

-

-

44.071%

2022-04-27T23:27:09

Oliver Kruse

Threadripper-PC

30000000

10035812696910

skipped known factor: 7364843617
skipped known factor: 2059086847566011497673

5,418

-

-

63.174%

ECM factoring results:

Old Calculation Method

Total ECM effort:	12.027 GHz-days
Estimated T-Level:	27.102

Digits	B1	Curves	Complete	FacMiss
20	11000	550 / 100	5.500	0.398%
25	50000	550 / 280	1.964	13.976%
30	250000	269 / 640	0.420	65.663%

New Calculation Method

Total ECM effort:	12.027 GHz-days
Estimated T-Level:	27.102

Digits	B1	Complete	FacMiss
20	11000	35.580	0.000%
25	50000	4.826	0.802%
30	250000	0.486	61.492%
35	1000000	0.039	96.192%
40	3000000	0.003	99.745%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		206	1.501
50000	5000000	2059086847566011497673	75	0.547
250000	25000000		227	8.271
250000	25000000	216797667997308422734706119	7	0.255
250000	34266310		7	0.286
250000	34750000		7	0.288
250000	35105348		14	0.579
250000	38500000		7	0.301

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
2015-01-09T16:37:00	TJAOI	Manual testing	50000	5000000						50	0.364
2016-03-11T13:48:15	TJAOI	Manual testing	50000	5000000	2059086847566011497673	70.802	75	2		75	0.547
2016-03-11T13:48:16	TJAOI	Manual testing	50000	5000000						106	0.772
2017-07-14T09:29:13	TJAOI	Manual testing	250000	25000000						44	1.603
2020-01-07T09:43:32	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.109
2020-01-09T14:55:11	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.109
2020-01-11T20:50:46	kracker	O0	250000	25000000						3	0.109
2020-01-14T00:59:41	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.109
2020-01-16T05:18:53	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.109
2020-01-18T11:25:02	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.109
2020-01-20T20:39:15	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.109
2020-01-23T05:54:42	kracker	O0	250000	25000000						3	0.109
2020-01-25T14:00:22	kracker	O0	250000	25000000						3	0.109
2020-01-28T00:49:49	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.109
2020-01-30T16:37:32	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.109
2020-02-02T15:05:00	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.109
2020-02-05T17:28:49	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.109
2020-02-08T23:18:30	Jay G.	Optiplex	250000	25000000						3	0.109
2020-02-13T06:09:47	_p95holder_	TFL17_PRPt12pE_k	250000	25000000						3	0.109
2020-02-16T06:32:32	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.109
2020-02-19T09:43:23	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.109
2020-02-22T23:00:46	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.109
2020-02-26T11:38:56	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.109
2020-02-29T23:24:48	kracker	O0	250000	25000000						3	0.109
2020-03-05T18:37:38	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.109
2020-03-11T08:51:59	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.109
2020-03-17T02:38:58	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.109
2020-03-22T16:34:31	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.109
2020-04-12T07:16:26	Oliver Kruse	Melissa	250000	25000000						3	0.109
2020-04-29T03:12:43	Greg	azure2	250000	25000000						3	0.109
2020-05-03T09:07:19	kracker	O0	250000	25000000						3	0.109
2020-05-09T08:45:14	kracker	O0	250000	25000000						3	0.109
2020-05-27T21:26:46	-Anonymous-	aws-nano	250000	25000000						3	0.109
2020-06-14T12:50:31	_p95holder_	TFL18_PRPt12pE_m	250000	25000000						3	0.109
2020-06-15T09:53:01	TJAOI	Manual testing	250000	25000000						16	0.583
2020-10-08T09:17:58	nordi	sweet16	250000	25000000						7	0.255
2020-10-31T20:06:53	nordi	sweet16	250000	25000000						7	0.255
2020-11-25T20:29:07	MarkS	desktop-i7	250000	25000000						7	0.255
2021-01-19T04:27:37	seatsea	dt	250000	35105348						7	0.289
2021-02-14T08:58:34	mnd9	consult	250000	25000000						7	0.255
2021-04-10T21:02:53	_p95holder_	TFL18_PRPt12pE_m	250000	25000000						7	0.255
2021-05-31T23:09:12	_p95holder_	TFL15_PRPt13pE_s	250000	25000000						7	0.255
2021-07-13T01:34:48	MarkS	laptop64	250000	25000000						7	0.255
2021-07-14T09:01:31	seatsea	Manual testing	250000	35105348						7	0.289
2021-09-22T11:35:02	happy5214	Focus	250000	38500000						7	0.301
2021-11-05T22:38:39	mnd9	f4	250000	25000000						7	0.255
2022-01-13T18:04:22	_p95holder_	TFL15_PRPt13pE_s	250000	25000000						7	0.255
2022-03-13T17:58:41	Alex Kruppa	lily	250000	34750000						7	0.288
2022-05-14T22:26:09	Corey	tab	250000	25000000	216797667997308422734706119	87.486	7	2	4325952875789418	7	0.255
2022-06-04T16:41:02	Corey	tab	250000	25000000						7	0.255
2022-07-01T15:07:52	debrouxl	z400	250000	34266310						7	0.286
2022-07-26T14:09:10	Corey	tab	250000	25000000						7	0.255

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