M1952663 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	15.2171	68.6567%	500000	15000000	0.1015	5.1083%	15.3186	70.2578%	1.6011%
PrimeNet	2⁵⁸	0.0197	63.7931%	8000	140000	0.0012	2.4674%	0.0209	64.6865%	0.8934%
GPU72	2⁶²	0.3146	66.1290%	8000	90000	0.0010	1.1534%	0.3156	66.5197%	0.3907%
Difference	+5	+14.9025	+2.5277%	+492000	+14910000	+0.1005	+3.9549%	+15.0030	+3.7381%	+3.7381%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

15.2171

68.6567%

500000

15000000

0.1015

5.1083%

15.3186

70.2578%

1.6011%

PrimeNet

2⁵⁸

0.0197

63.7931%

8000

140000

0.0012

2.4674%

0.0209

64.6865%

0.8934%

GPU72

2⁶²

0.3146

66.1290%

8000

90000

0.0010

1.1534%

0.3156

66.5197%

0.3907%

Difference

+14.9025

+2.5277%

+492000

+14910000

+0.1005

+3.9549%

+15.0030

+3.7381%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1952663	3905327	7	21.897	1 1	-	1	1	1.431e-13	7.866e-8	1.601e-7
1952663	643997908213602201929	21	69.126	164902471192828 2² × 17 × 41 × 1427 × 41448653	2021-02-22	1427	41448653	114.00	0.1777	0.3318

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

1952663

3905327

21.897

1
1

1.431e-13

7.866e-8

1.601e-7

1952663

643997908213602201929

69.126

164902471192828
2² × 17 × 41 × 1427 × 41448653

2021-02-22

1427

41448653

114.00

0.1777

0.3318

exponent	prime factors	composite factor	digits	bits*
1952663	3905327 643997908213602201929	2515022418890102446452775783	28	91.023

exponent

prime factors

composite factor

digits

bits*

1952663

3905327
643997908213602201929

2515022418890102446452775783

91.023

	GHz-Days	worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved
2016-03-17T19:19:14	alpertron	Manual testing	500000	15000000	12	-	skipped known factor: 3905327	-	-	0.101	-	-	5.108%

GHz-Days

worth

Factor
probability

date

userid

compid

stage

factor

digits

bits*

spent

saved

2016-03-17T19:19:14

alpertron

Manual testing

500000

15000000

skipped known factor: 3905327

0.101

-

-

5.108%

ECM factoring results:

Old Calculation Method

Total ECM effort:	21.052 GHz-days
Estimated T-Level:	24.589

Digits	B1	Curves	Complete	FacMiss
20	11000	257 / 100	2.570	7.555%
25	50000	257 / 280	0.918	39.872%

New Calculation Method

Total ECM effort:	21.052 GHz-days
Estimated T-Level:	24.589

Digits	B1	Complete	FacMiss
20	11000	10.622	0.002%
25	50000	1.004	36.645%
30	250000	0.064	93.799%
35	1000000	0.003	99.699%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		25	1.740
50000	5000000	643997908213602201929	2	0.139
50000	6750000		7	0.556
50000	6900000		7	0.562
50000	7500000		216	18.06

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2016-07-18T07:27:19	Richard B. Woods	Puttputt	50000	5000000						1	0.070
2018-05-21T12:53:14	Oliver Kruse	ECM-HTC	50000	5000000						3	0.209
2020-11-24T12:57:11	MarkS	desktop-i7	50000	5000000						7	0.487
2021-02-22T02:28:41	Kublenz	Medion_E4272	50000	5000000	643997908213602201929	69.126	2	2	655023566595293	2	0.139
2021-04-04T23:52:57	Poao	justg-ZA	50000	5000000						7	0.487
2021-07-15T14:16:49	_p95holder_	TFL18_PRPt12pE_m	50000	5000000						7	0.487
2021-09-29T12:17:24	Dylan Delgado	laptop-ryzen73700	50000	6750000						7	0.556
2022-02-21T06:16:54	MarkS	desktop-i7	50000	6900000						7	0.562
2022-05-12T09:17:48	TJAOI	Manual testing	50000	7500000						216	18.06

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-05T05:51:50

Oliver Kruse

GTX-0

3905327

52C520ED25D75C__

2017-11-11T14:17:39

kkmrkkblmbrbk

c4.xlarge

3905327

52C520ED25D75C__

2021-02-23T21:25:36

Cork

3tits

3905327

643997908213602201929

E6902D81501B05B9

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