M267373 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	20000000	1820000000	1.1699	51.1527%	1.1699	51.1527%	51.1527%
PrimeNet	2⁴⁰	0.0000	52.5000%	2800	70000	0.0001	14.4594%	0.0001	59.3682%	6.8682%
GPU72	2⁴⁴	0.0000	56.8182%	5000	120000	0.0001	10.5964%	0.0001	61.3939%	4.5757%
Difference	-44	0.0000	-56.8182%	+19995000	+1819880000	+1.1698	+40.5563%	+1.1697	-10.2412%	-10.2412%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

unknown

20000000

1820000000

1.1699

51.1527%

1.1699

51.1527%

PrimeNet

2⁴⁰

0.0000

52.5000%

2800

70000

0.0001

14.4594%

0.0001

59.3682%

6.8682%

GPU72

2⁴⁴

0.0000

56.8182%

5000

120000

0.0001

10.5964%

0.0001

61.3939%

4.5757%

Difference

-44

0.0000

-56.8182%

+19995000

+1819880000

+1.1698

+40.5563%

+1.1697

-10.2412%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
267373	6859721689	10	32.676	12828 2² × 3 × 1069	-	4	1069	3.802e-9	6.146e-7	1.074e-6
267373	6467292678485830185630192103	28	92.385	12094139420371223320287 3 × 7 × 13 × 7529 × 39292609 × 149749079	2020-04-02	39292609	149749079	4.212e+9	0.4490	0.7923

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

267373

6859721689

32.676

12828
2² × 3 × 1069

1069

3.802e-9

6.146e-7

1.074e-6

267373

6467292678485830185630192103

92.385

12094139420371223320287
3 × 7 × 13 × 7529 × 39292609 × 149749079

2020-04-02

39292609

149749079

4.212e+9

0.4490

0.7923

exponent	prime factors	composite factor	digits	bits*
267373	6859721689 6467292678485830185630192103	44363827855720153003538324902185621967	38	125.061

exponent

prime factors

composite factor

digits

bits*

267373

6859721689
6467292678485830185630192103

44363827855720153003538324902185621967

125.061

	GHz-Days	worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved
2021-07-03T16:08:53	George Woltman	Manual testing	20000000	1820000000		-	skipped known factor: 6859721689	-	-	1.170	-	-	42.670%

GHz-Days

worth

Factor
probability

date

userid

compid

stage

factor

digits

bits*

spent

saved

2021-07-03T16:08:53

George Woltman

Manual testing

20000000

1820000000

skipped known factor: 6859721689

1.170

-

-

42.670%

date	userid	compid	b1	b2	start	factor	Smooth	digits	bits*	ghz-days
2021-07-03T16:08:53	George Woltman	Manual testing	10000000	830000000	2	7			-	-	0.506

date

userid

compid

start

factor

Smooth

digits

bits*

ghz-days

2021-07-03T16:08:53

George Woltman

Manual testing

10000000

830000000

0.506

ECM factoring results:

Old Calculation Method

Total ECM effort:	8.985 GHz-days
Estimated T-Level:	26.469

Digits	B1	Curves	Complete	FacMiss
20	11000	469 / 100	4.690	0.897%
25	50000	469 / 280	1.675	18.675%
30	250000	188 / 640	0.294	74.529%

New Calculation Method

Total ECM effort:	8.985 GHz-days
Estimated T-Level:	26.469

Digits	B1	Complete	FacMiss
20	11000	24.731	0.000%
25	50000	3.091	4.547%
30	250000	0.296	74.398%
35	1000000	0.023	97.755%
40	3000000	0.001	99.855%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		281	2.051
250000	25000000		149	5.436
250000	25000000	6467292678485830185630192103	25	0.912
250000	35250000		7	0.290
250000	36750000		7	0.295

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2014-09-05T15:15:00	TJAOI	Manual testing	50000	5000000						50	0.365
2015-02-27T10:12:00	TJAOI	Manual testing	50000	5000000						50	0.365
2015-10-02T10:44:06	TJAOI	Manual testing	50000	5000000						90	0.657
2016-08-05T12:39:02	TJAOI	Manual testing	50000	5000000						91	0.664
2017-12-01T13:33:20	TJAOI	Manual testing	250000	25000000						44	1.605
2020-01-29T02:18:20	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.109
2020-01-31T20:22:35	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.109
2020-02-03T20:51:08	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.109
2020-02-06T23:54:42	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.109
2020-02-10T08:53:29	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.109
2020-02-13T22:16:02	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.109
2020-02-17T20:00:13	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.109
2020-02-20T22:05:26	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.109
2020-02-24T19:40:33	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.109
2020-02-27T22:02:27	kracker	O0	250000	25000000						3	0.109
2020-03-03T00:12:00	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.109
2020-03-07T18:25:39	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.109
2020-03-13T17:23:34	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.109
2020-03-19T07:23:30	Niels_Mache_Nextcloud	SuperDry-Y	250000	25000000						3	0.109
2020-04-02T19:27:16	nordi	sweet16	250000	25000000	6467292678485830185630192103	92.385	25	2	8325019008617517	25	0.912
2020-07-17T05:14:21	_p95holder_	TFL1_PRPt8pE_n	250000	25000000						3	0.109
2020-07-25T21:14:03	_p95holder_	TFL18_PRPt12pE_m	250000	25000000						3	0.109
2020-08-15T01:28:01	volki	home	250000	25000000						3	0.109
2020-09-18T09:12:22	TJAOI	Manual testing	250000	25000000						33	1.204
2021-03-01T11:38:27	_p95holder_	TFL1_PRPt8pE_n	250000	25000000						7	0.255
2021-04-24T01:47:12	Chang Chia-Tche	exbpc13	250000	25000000						7	0.255
2021-06-09T06:26:07	Ducho_YYZ	Dutch	250000	35250000						7	0.290
2022-04-13T20:54:18	_p95holder_	TFL18_PRPt12pE_m	250000	25000000						7	0.255
2022-05-25T06:10:00	debrouxl	dl380g9-1	250000	36750000						7	0.295

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-22T09:24:02

Oliver Kruse

Ollaptop

6859721689

7EAE68DDC07344__

2017-09-22T10:07:19

Oliver Kruse

Manual testing

6859721689

7EAE68DDC07344__

2017-10-12T18:06:14

Oliver Kruse

GTX-2

7EAE68DDC07344__

2017-11-06T16:57:39

kkmrkkblmbrbk

c4.xlarge

6859721689

7EAE68DDC07344__

2020-04-03T09:01:06

trebor

Laptop

6859721689

6467292678485830185630192103

E4CE40EF9A4A515D

2020-04-03T11:48:31

mnd9

mnd

6859721689

6467292678485830185630192103

E4CE40EF9A4A515D

2020-04-03T17:39:58

Daniil Tsarkov

9900

6859721689

6467292678485830185630192103

E4CE40EF9A4A515D

2020-04-05T20:00:31

Luigi Morelli

9800X

6859721689

6467292678485830185630192103

E4CE40EF9A4A515D

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