M286243 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	50000	50000	0.0005	14.8793%	0.0005	14.8793%	14.8793%
PrimeNet	2⁴⁰	0.0000	52.5000%	3000	80000	0.0001	15.0573%	0.0001	59.6522%	7.1522%
GPU72	2⁴⁴	0.0000	56.8182%	5000	130000	0.0001	10.8747%	0.0001	61.5141%	4.6959%
Difference	-44	0.0000	-56.8182%	+45000	-80000	+0.0004	+4.0046%	+0.0004	-46.6348%	-46.6348%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

unknown

50000

0.0005

14.8793%

0.0005

14.8793%

PrimeNet

2⁴⁰

0.0000

52.5000%

3000

80000

0.0001

15.0573%

0.0001

59.6522%

7.1522%

GPU72

2⁴⁴

0.0000

56.8182%

5000

130000

0.0001

10.8747%

0.0001

61.5141%

4.6959%

Difference

-44

0.0000

-56.8182%

+45000

-80000

+0.0004

+4.0046%

+0.0004

-46.6348%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
286243	1360226737	10	30.341	2376 2³ × 3³ × 11	-	27	27	7.567e-10	2.675e-7	5.445e-7
286243	5408699513284985783	19	62.230	9447741103337 23 × 127 × 3234420097	2014-09-05	127	3234420097	4.8312	1.7460	3.2611
286243	131882387679537575824324937	27	86.769	230367882672305656076 2² × 61 × 1201489 × 785800508111	2020-06-26	1201489	785800508111	101,629,008	424.21	792.29

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

286243

1360226737

30.341

2376
2³ × 3³ × 11

7.567e-10

2.675e-7

5.445e-7

286243

5408699513284985783

62.230

9447741103337
23 × 127 × 3234420097

2014-09-05

127

3234420097

4.8312

1.7460

3.2611

286243

131882387679537575824324937

86.769

230367882672305656076
2² × 61 × 1201489 × 785800508111

2020-06-26

1201489

785800508111

101,629,008

424.21

792.29

exponent	prime factors	composite factor	digits	bits*
286243	1360226737 5408699513284985783	7357057690369124362701480071	28	92.571
286243	1360226737 131882387679537575824324937	179389949861106398432411594283240569	36	117.111
286243	5408699513284985783 131882387679537575824324937	713312206053176691942989429429872793617370671	45	148.999
286243	1360226737 5408699513284985783 131882387679537575824324937	97026633450198418016606670161888764038723053433383 0527	54	179.341

exponent

prime factors

composite factor

digits

bits*

286243

1360226737
5408699513284985783

7357057690369124362701480071

92.571

286243

1360226737
131882387679537575824324937

179389949861106398432411594283240569

117.111

286243

5408699513284985783
131882387679537575824324937

713312206053176691942989429429872793617370671

148.999

286243

1360226737
5408699513284985783
131882387679537575824324937

97026633450198418016606670161888764038723053433383
0527

179.341

	GHz-Days	worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved
2022-02-06T16:47:55	Lisander Viaene	Manual testing	50000	50000		-	skipped known factor: 1360226737	-	-	0.000	-	-	9.695%

GHz-Days

worth

Factor
probability

date

userid

compid

stage

factor

digits

bits*

spent

saved

2022-02-06T16:47:55

Lisander Viaene

Manual testing

50000

skipped known factor: 1360226737

0.000

-

-

9.695%

ECM factoring results:

Old Calculation Method

Total ECM effort:	17.728 GHz-days
Estimated T-Level:	28.063

Digits	B1	Curves	Complete	FacMiss
20	11000	673 / 100	6.730	0.115%
25	50000	673 / 280	2.404	9.001%
30	250000	392 / 640	0.613	54.173%

New Calculation Method

Total ECM effort:	17.728 GHz-days
Estimated T-Level:	28.063

Digits	B1	Complete	FacMiss
20	11000	41.731	0.000%
25	50000	5.648	0.353%
30	250000	0.574	56.336%
35	1000000	0.046	95.540%
40	3000000	0.003	99.701%

ECM Summary

B1	B2	factor	curves	GHz-days
		5408699513284985783	1	0.00000e+0
50000	5000000		281	2.056
250000	25000000		157	5.743
250000	25000000	131882387679537575824324937	1	0.037
250000	34250000		7	0.288
250000	36750000		227	9.61

	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	0.366
2014-09-05T15:16:00	TJAOI	Manual testing			5408699513284985783	62.230		1		1	-
2015-01-09T16:39:00	TJAOI	Manual testing	50000	5000000						50	0.366
2015-10-30T13:18:16	TJAOI	Manual testing	50000	5000000						90	0.658
2016-03-24T20:21:11	TJAOI	Manual testing	50000	5000000						91	0.666
2019-01-04T14:23:58	TJAOI	Manual testing	250000	25000000						44	1.609
2020-04-28T22:59:51	Greg	azure3	250000	25000000						3	0.110
2020-05-03T02:06:36	Greg Hogan	azure4	250000	25000000						3	0.110
2020-05-09T00:27:49	Greg Hogan	azure3	250000	25000000						3	0.110
2020-06-09T05:27:51	_p95holder_	TFL18_PRPt12pE_m	250000	25000000						3	0.110
2020-06-14T02:36:36	nordi	sweet16	250000	25000000						3	0.110
2020-06-25T05:09:10	nordi	sweet16	250000	25000000	131882387679537575824324937	86.769	1	2	7879176830883165	1	0.037
2020-07-01T17:59:21	nordi	sweet16	250000	25000000						3	0.110
2020-07-10T12:27:14	kracker	O0	250000	25000000						3	0.110
2020-07-23T09:50:35	Chang Chia-Tche	exbpc13	250000	25000000						3	0.110
2020-08-05T09:45:42	_p95holder_	TFL15_PRPt13pE_s	250000	25000000						3	0.110
2020-09-16T17:49:44	nordi	sweet16	250000	25000000						7	0.256
2020-10-24T04:59:39	nordi	sweet16	250000	25000000						7	0.256
2020-11-07T18:42:38	nordi	sweet16	250000	25000000						7	0.256
2021-01-01T10:28:18	TJAOI	Manual testing	250000	25000000						51	1.865
2021-01-01T22:56:25	_p95holder_	TFL17_PRPt12pE_k	250000	25000000						7	0.256
2021-12-03T20:10:11	Luminescence	W-2295	250000	36750000						7	0.296
2022-02-22T00:38:17	Corey	tab	250000	25000000						7	0.256
2022-04-12T19:20:13	Team_Inspector	SpudBoy4	250000	34250000						7	0.288
2022-04-28T12:36:22	nordi	sweet16_ccx2	250000	36750000						220	9.310

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-22T12:32:07

Oliver Kruse

Doppelherz

1360226737

5408699513284985783

2EBDBE98CE959B__

2017-09-22T20:36:28

Oliver Kruse

Manual testing

1360226737

5408699513284985783

2EBDBE98CE959B__

2017-09-24T17:45:26

Oliver Kruse

Manual testing

1360226737

5408699513284985783

2EBDBE98CE959B__

2017-11-06T20:03:12

kkmrkkblmbrbk

c4.xlarge

1360226737

5408699513284985783

2EBDBE98CE959B__

2020-04-17T22:10:23

Oliver Kruse

AddPrpType5

1360226737

5408699513284985783

907B8670B406C4__

2020-06-25T05:20:31

CrypticClue

Manual testing

1360226737

5408699513284985783

131882387679537575824324937

907B8670B406C4F8

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