M1760557 Mersenne number exponent details

Residue

Status

L-L

094B42FC558E229D

double-checked

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	16.8776	68.6567%	500000	15000000	0.1015	5.0450%	16.9790	70.2380%	1.5813%
PrimeNet	2⁵⁷	0.0109	63.1579%	8000	140000	0.0012	2.8057%	0.0121	64.1916%	1.0337%
GPU72	2⁶¹	0.1745	65.5738%	8000	120000	0.0011	1.4527%	0.1756	66.0739%	0.5001%
Difference	+6	+16.7031	+3.0829%	+492000	+14880000	+0.1004	+3.5923%	+16.8035	+4.1641%	+4.1641%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

16.8776

68.6567%

500000

15000000

0.1015

5.0450%

16.9790

70.2380%

1.5813%

PrimeNet

2⁵⁷

0.0109

63.1579%

8000

140000

0.0012

2.8057%

0.0121

64.1916%

1.0337%

GPU72

2⁶¹

0.1745

65.5738%

8000

120000

0.0011

1.4527%

0.1756

66.0739%

0.5001%

Difference

+16.7031

+3.0829%

+492000

+14880000

+0.1004

+3.5923%

+16.8035

+4.1641%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1760557	247441355198856473	18	57.780	70273599548 2² × 31 × 566722577	-	31	566722577	0.0200	2.4288	4.5364
1760557	481040135977258046234743	24	78.671	136615893713540103 3 × 4049 × 11246883486749	2019-08-04	4049	11246883486749	52,857	48,201	90,027

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

1760557

247441355198856473

57.780

70273599548
2² × 31 × 566722577

566722577

0.0200

2.4288

4.5364

1760557

481040135977258046234743

78.671

136615893713540103
3 × 4049 × 11246883486749

2019-08-04

4049

11246883486749

52,857

48,201

90,027

exponent	prime factors	composite factor	digits	bits*
1760557	247441355198856473 481040135977258046234743	119029223151254924956855399281876923041439	42	136.450

exponent

prime factors

composite factor

digits

bits*

1760557

247441355198856473
481040135977258046234743

119029223151254924956855399281876923041439

136.450

	GHz-Days	worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved
2016-03-16T12:30:16	alpertron	Manual testing	500000	15000000	12	-		-	-	0.101	-	-	5.045%

GHz-Days

worth

Factor
probability

date

userid

compid

stage

factor

digits

bits*

spent

saved

2016-03-16T12:30:16

alpertron

Manual testing

500000

15000000

0.101

-

-

5.045%

ECM factoring results:

Old Calculation Method

Total ECM effort:	17.881 GHz-days
Estimated T-Level:	24.643

Digits	B1	Curves	Complete	FacMiss
20	11000	260 / 100	2.600	7.331%
25	50000	260 / 280	0.929	39.446%

New Calculation Method

Total ECM effort:	17.881 GHz-days
Estimated T-Level:	24.643

Digits	B1	Complete	FacMiss
20	11000	8.387	0.023%
25	50000	0.758	46.859%
30	250000	0.047	95.439%
35	1000000	0.002	99.786%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		257	17.68
50000	5000000	481040135977258046234743	3	0.206

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2017-06-11T18:51:18	Richard B. Woods	Puttputt	50000	5000000						1	0.069
2018-03-21T15:17:18	Alvin Bunk	WorkCAT	50000	5000000						3	0.206
2019-08-04T11:46:36	Chang Chia-Tche	exbpc13	50000	5000000	481040135977258046234743	78.671	3	2		3	0.206
2020-02-28T08:19:24	Niels_Mache_Nextcloud	SuperDry-Y	50000	5000000						3	0.206
2020-03-10T05:18:46	Niels_Mache_Nextcloud	SuperDry-Y	50000	5000000						3	0.206
2020-03-23T08:24:01	Niels_Mache_Nextcloud	SuperDry-Y	50000	5000000						3	0.206
2020-05-03T09:23:49	Bommer	3770K	50000	5000000						3	0.206
2020-05-23T15:50:27	_p95holder_	TFL15_PRPt13pE_s	50000	5000000						3	0.206
2020-06-24T19:29:48	kracker	O0	50000	5000000						3	0.206
2020-07-22T11:51:30	-Anonymous-	aws	50000	5000000						3	0.206
2020-08-28T11:15:51	TJAOI	Manual testing	50000	5000000						232	15.96

date	userid	compid	res64	spent (GHz-days)
1999-09-14T00:00:00	ANONYMOUS	v4_computers	094B42FC558E229D	0.096

date

userid

compid

res64

spent (GHz-days)

1999-09-14T00:00:00

ANONYMOUS

v4_computers

094B42FC558E229D

0.096

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-03T09:16:02

Oliver Kruse

GTX-3

247441355198856473

537306C883219D__

2017-11-04T02:26:08

kkmrkkblmbrbk

c4.xlarge

247441355198856473

537306C883219D__

2019-08-08T15:16:08

roemer2201

ws-rebentrost-o

247441355198856473

481040135977258046234743

F3CB5598CEA0DF43

2019-08-09T14:19:25

kkmrkkblmbrbk

c5.large

247441355198856473

481040135977258046234743

F3CB5598CEA0DF43

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

10⁹

10¹⁰

10¹¹

10¹²

10¹³

10¹⁴

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