M1969757 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	15.0851	68.6567%	132000	134381520	0.7099	5.8649%	15.7950	70.4950%	1.8383%
PrimeNet	2⁵⁸	0.0195	63.7931%	8000	140000	0.0014	2.4716%	0.0209	64.6880%	0.8949%
GPU72	2⁶²	0.3119	66.1290%	8000	100000	0.0012	1.1959%	0.3131	66.5341%	0.4050%
Difference	+5	+14.7732	+2.5277%	+124000	+134281520	+0.7087	+4.6691%	+15.4818	+3.9609%	+3.9609%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

15.0851

68.6567%

132000

134381520

0.7099

5.8649%

15.7950

70.4950%

1.8383%

PrimeNet

2⁵⁸

0.0195

63.7931%

8000

140000

0.0014

2.4716%

0.0209

64.6880%

0.8949%

GPU72

2⁶²

0.3119

66.1290%

8000

100000

0.0012

1.1959%

0.3131

66.5341%

0.4050%

Difference

+14.7732

+2.5277%

+124000

+134281520

+0.7087

+4.6691%

+15.4818

+3.9609%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1969757	7957089501426113	16	52.821	2019815008 2⁵ × 63119219	-	32	63119219	0.0004	0.3279	0.6123
1969757	365326984500560808151	21	68.308	92734023663975 3 × 5² × 1236453648853	2021-07-16	25	1236453648853	41.395	6,422.4	11,995

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

1969757

7957089501426113

52.821

2019815008
2⁵ × 63119219

63119219

0.0004

0.3279

0.6123

1969757

365326984500560808151

68.308

92734023663975
3 × 5² × 1236453648853

2021-07-16

1236453648853

41.395

6,422.4

11,995

exponent	prime factors	composite factor	digits	bits*
1969757	7957089501426113 365326984500560808151	2906939512957072712496884790294647063	37	121.129

exponent

prime factors

composite factor

digits

bits*

1969757

7957089501426113
365326984500560808151

2906939512957072712496884790294647063

121.129

	GHz-Days	worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved
2022-08-12T10:08:05	harlee	i5-5250U_1600	132000	134381520		-	skipped known factor: 7957089501426113	-	-	0.710	-	-	5.865%

GHz-Days

worth

Factor
probability

date

userid

compid

stage

factor

digits

bits*

spent

saved

2022-08-12T10:08:05

harlee

i5-5250U_1600

132000

134381520

skipped known factor: 7957089501426113

0.710

-

-

5.865%

ECM factoring results:

Old Calculation Method

Total ECM effort:	26.134 GHz-days
Estimated T-Level:	24.732

Digits	B1	Curves	Complete	FacMiss
20	11000	265 / 100	2.650	6.972%
25	50000	265 / 280	0.946	38.747%

New Calculation Method

Total ECM effort:	26.134 GHz-days
Estimated T-Level:	24.732

Digits	B1	Complete	FacMiss
20	11000	10.908	0.002%
25	50000	1.030	35.689%
30	250000	0.066	93.644%
35	1000000	0.003	99.691%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		38	3.208
50000	5850000		7	0.631
50000	6650000	365326984500560808151	4	0.383
50000	7500000		216	21.91

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2017-12-21T19:32:12	alpertron	laptop2	50000	5000000						3	0.253
2019-03-26T05:34:57	ATH	ec2-ECMCF	50000	5000000						3	0.253
2021-01-23T14:21:43	MarkS	desktop-i7	50000	5000000						11	0.929
2021-07-16T12:06:38	seatsea	dt	50000	6650000	365326984500560808151	68.308	4	2	6781714808123667	4	0.383
2021-08-25T20:14:24	_p95holder_	TFL17_PRPt12pE_k	50000	5000000						7	0.591
2021-11-29T07:13:50	_p95holder_	TFL17_PRPt12pE_k	50000	5000000						7	0.591
2022-04-18T06:56:39	_p95holder_	TFL18_PRPt12pE_m	50000	5000000						7	0.591
2022-06-28T02:11:31	Eric	miniPCWindows	50000	5850000						7	0.631
2022-07-14T08:09:33	TJAOI	Manual testing	50000	7500000						216	21.91

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-05T10:08:59

Oliver Kruse

GTX-3

7957089501426113

C204AF9A72BFF8__

2017-11-12T03:28:39

kkmrkkblmbrbk

c4.xlarge

7957089501426113

C204AF9A72BFF8__

2021-07-16T13:02:41

GURA LOVE

7957089501426113

365326984500560808151

90A051FE32F24F31

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 = 132000, B2 = 134381520 (P-1 stage 2)

B1 = 132000 (P-1 stage 1)

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

10¹²

10¹³

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