M1770973 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	16.7783	68.6567%	500000	15000000	0.1015	5.0486%	16.8798	70.2391%	1.5824%
PrimeNet	2⁵⁷	0.0108	63.1579%	8000	140000	0.0012	2.8088%	0.0120	64.1927%	1.0348%
GPU72	2⁶¹	0.1735	65.5738%	8000	120000	0.0011	1.4545%	0.1746	66.0745%	0.5007%
Difference	+6	+16.6048	+3.0829%	+492000	+14880000	+0.1004	+3.5941%	+16.7052	+4.1646%	+4.1646%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

16.7783

68.6567%

500000

15000000

0.1015

5.0486%

16.8798

70.2391%

1.5824%

PrimeNet

2⁵⁷

0.0108

63.1579%

8000

140000

0.0012

2.8088%

0.0120

64.1927%

1.0348%

GPU72

2⁶¹

0.1735

65.5738%

8000

120000

0.0011

1.4545%

0.1746

66.0745%

0.5007%

Difference

+16.6048

+3.0829%

+492000

+14880000

+0.1004

+3.5941%

+16.7052

+4.1646%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1770973	4586972373679	13	42.061	1295043 3 × 17 × 67 × 379	-	67	379	4.342e-7	6.608e-6	1.073e-5
1770973	6141657926883715120513	22	72.379	1733978419457472 2⁶ × 3² × 73 × 41238071239	2020-08-13	73	41238071239	850.04	176.74	330.09

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

1770973

4586972373679

42.061

1295043
3 × 17 × 67 × 379

379

4.342e-7

6.608e-6

1.073e-5

1770973

6141657926883715120513

72.379

1733978419457472
2⁶ × 3² × 73 × 41238071239

2020-08-13

41238071239

850.04

176.74

330.09

exponent	prime factors	composite factor	digits	bits*
1770973	4586972373679 6141657926883715120513	28171615239202240973749539154177327	35	114.440

exponent

prime factors

composite factor

digits

bits*

1770973

4586972373679
6141657926883715120513

28171615239202240973749539154177327

114.440

	GHz-Days	worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved
2016-03-16T12:31:17	alpertron	Manual testing	500000	15000000	12	-	skipped known factor: 4586972373679	-	-	0.101	-	-	5.049%

GHz-Days

worth

Factor
probability

date

userid

compid

stage

factor

digits

bits*

spent

saved

2016-03-16T12:31:17

alpertron

Manual testing

500000

15000000

skipped known factor: 4586972373679

0.101

-

-

5.049%

ECM factoring results:

Old Calculation Method

Total ECM effort:	17.274 GHz-days
Estimated T-Level:	24.482

Digits	B1	Curves	Complete	FacMiss
20	11000	251 / 100	2.510	8.025%
25	50000	251 / 280	0.896	40.737%

New Calculation Method

Total ECM effort:	17.274 GHz-days
Estimated T-Level:	24.482

Digits	B1	Complete	FacMiss
20	11000	8.097	0.030%
25	50000	0.732	48.105%
30	250000	0.045	95.594%
35	1000000	0.002	99.794%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		248	17.07
50000	5000000	6141657926883715120513	3	0.206

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2017-08-06T16:51:15	Richard B. Woods	Puttputt	50000	5000000						1	0.069
2018-03-25T23:22:37	Oliver Kruse	ECM-HTC	50000	5000000						3	0.206
2019-08-21T01:32:17	Chang Chia-Tche	exbpc13	50000	5000000						3	0.206
2020-03-05T06:08:02	Niels_Mache_Nextcloud	SuperDry-Y	50000	5000000						3	0.206
2020-03-17T21:20:43	Niels_Mache_Nextcloud	SuperDry-Y	50000	5000000						3	0.206
2020-04-17T20:02:15	kracker	O0	50000	5000000						3	0.206
2020-05-07T09:46:15	Greg Hogan	azure2	50000	5000000						3	0.206
2020-06-14T23:28:39	_p95holder_	TFL15_PRPt13pE_s	50000	5000000						3	0.206
2020-07-10T20:00:19	MarkS	desktop-i7	50000	5000000						3	0.206
2020-08-13T01:23:12	Chang Chia-Tche	exbpc13	50000	5000000	6141657926883715120513	72.379	3	2		3	0.206
2020-09-18T09:19:15	TJAOI	Manual testing	50000	5000000						184	12.66
2020-09-18T09:20:02	TJAOI	Manual testing	50000	5000000						39	2.684

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-03T11:38:03

Oliver Kruse

GTX-3

4586972373679

0E8BFFEB55A21C__

2017-11-04T09:49:51

kkmrkkblmbrbk

c4.xlarge

4586972373679

0E8BFFEB55A21C__

2020-08-15T07:45:13

Team_Inspector

SpudBoy4

4586972373679

6141657926883715120513

2EF7C95E8258AA4D

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

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