M1929043 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	2⁶⁷	15.4035	68.6567%	500000	15000000	0.1015	5.1008%	15.5049	70.2555%	1.5988%
PrimeNet	2⁵⁷	0.0100	63.1579%	9000	170000	0.0014	3.0955%	0.0114	64.2983%	1.1404%
GPU72	2⁶¹	0.1592	65.5738%	11000	170000	0.0015	1.8146%	0.1608	66.1985%	0.6247%
Difference	+6	+15.2442	+3.0829%	+489000	+14830000	+0.0999	+3.2862%	+15.3441	+4.0570%	+4.0570%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

15.4035

68.6567%

500000

15000000

0.1015

5.1008%

15.5049

70.2555%

1.5988%

PrimeNet

2⁵⁷

0.0100

63.1579%

9000

170000

0.0014

3.0955%

0.0114

64.2983%

1.1404%

GPU72

2⁶¹

0.1592

65.5738%

11000

170000

0.0015

1.8146%

0.1608

66.1985%

0.6247%

Difference

+15.2442

+3.0829%

+489000

+14830000

+0.0999

+3.2862%

+15.3441

+4.0570%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1929043	312504967	9	28.219	81 3⁴	-	81	81	1.886e-11	6.372e-6	1.297e-5
1929043	158237239752253307537833	24	77.066	41014440775102812 2² × 3 × 2663 × 593171 × 2163737	2020-11-04	593171	2163737	25,181	0.0534	0.0950

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

1929043

312504967

28.219

81
3⁴

1.886e-11

6.372e-6

1.297e-5

1929043

158237239752253307537833

77.066

41014440775102812
2² × 3 × 2663 × 593171 × 2163737

2020-11-04

593171

2163737

25,181

0.0534

0.0950

exponent	prime factors	composite factor	digits	bits*
1929043	312504967 158237239752253307537833	49449923386949008047751352916511	32	105.286

exponent

prime factors

composite factor

digits

bits*

1929043

312504967
158237239752253307537833

49449923386949008047751352916511

105.286

	GHz-Days	worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved
2016-03-17T19:19:07	alpertron	Manual testing	500000	15000000	12	-	skipped known factor: 312504967	-	-	0.101	-	-	5.101%

GHz-Days

worth

Factor
probability

date

userid

compid

stage

factor

digits

bits*

spent

saved

2016-03-17T19:19:07

alpertron

Manual testing

500000

15000000

skipped known factor: 312504967

0.101

-

-

5.101%

ECM factoring results:

Old Calculation Method

Total ECM effort:	19.844 GHz-days
Estimated T-Level:	24.607

Digits	B1	Curves	Complete	FacMiss
20	11000	258 / 100	2.580	7.480%
25	50000	258 / 280	0.921	39.729%

New Calculation Method

Total ECM effort:	19.844 GHz-days
Estimated T-Level:	24.607

Digits	B1	Complete	FacMiss
20	11000	8.801	0.015%
25	50000	0.797	45.068%
30	250000	0.049	95.190%
35	1000000	0.002	99.774%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	4900000		7	0.483
50000	5000000		34	2.363
50000	5000000	158237239752253307537833	2	0.139
50000	6600000		215	16.86

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2017-12-20T06:31:45	alpertron	laptop2	50000	5000000						3	0.208
2019-02-09T14:14:21	oodaira	com1	50000	5000000						3	0.208
2020-11-04T06:00:16	nordi	sweet16	50000	5000000	158237239752253307537833	77.066	2	2	1436659850771951	2	0.139
2020-11-28T17:49:13	nordi	sweet16	50000	5000000						7	0.486
2021-02-26T20:08:36	Ducho_YYZ	oracle2	50000	4900000						7	0.483
2021-06-17T11:12:16	_p95holder_	TFL18_PRPt12pE_m	50000	5000000						7	0.486
2021-09-14T10:13:29	_p95holder_	TFL17_PRPt12pE_k	50000	5000000						7	0.486
2022-01-04T22:23:39	_p95holder_	TFL15_PRPt13pE_s	50000	5000000						7	0.486
2022-02-17T11:38:03	TJAOI	Manual testing	50000	6600000						215	16.86

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-05T00:50:36

Oliver Kruse

GTX-0

312504967

52F75DF730885D__

2017-11-10T13:01:03

kkmrkkblmbrbk

c4.xlarge

312504967

52F75DF730885D__

2020-11-04T06:15:25

ATH

ec2-PRPCF

312504967

158237239752253307537833

48BFC02AACE7B60F

P-1 factor-bounds graph:

X = B1; Y = B2
size of marker relates to size of factor
mouse-over any factor marker (circle) to see additional info
mouse-over any stage bound text to see additional info

B1 = 500000, B2 = 15000000 (P-1 stage 2)

B1 = 500000 (P-1 stage 1)

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

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