M1789373 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	16.6058	68.6567%	500000	15000000	0.1015	5.0549%	16.7072	70.2411%	1.5844%
PrimeNet	2⁵⁷	0.0107	63.1579%	8000	140000	0.0012	2.8143%	0.0119	64.1947%	1.0368%
GPU72	2⁶¹	0.1717	65.5738%	8000	130000	0.0012	1.4933%	0.1728	66.0878%	0.5141%
Difference	+6	+16.4341	+3.0829%	+492000	+14870000	+0.1003	+3.5616%	+16.5344	+4.1532%	+4.1532%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

16.6058

68.6567%

500000

15000000

0.1015

5.0549%

16.7072

70.2411%

1.5844%

PrimeNet

2⁵⁷

0.0107

63.1579%

8000

140000

0.0012

2.8143%

0.0119

64.1947%

1.0368%

GPU72

2⁶¹

0.1717

65.5738%

8000

130000

0.0012

1.4933%

0.1728

66.0878%

0.5141%

Difference

+16.4341

+3.0829%

+492000

+14870000

+0.1003

+3.5616%

+16.5344

+4.1532%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1789373	331386679682063	15	48.236	92598547 92598547	-	1	92598547	4.140e-5	0.3969	0.7412
1789373	177491689478873969399	21	67.266	49596056685463 49596056685463	2017-12-13	1	49596056685463	27.392	212,556	396,996

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

1789373

331386679682063

48.236

92598547
92598547

92598547

4.140e-5

0.3969

0.7412

1789373

177491689478873969399

67.266

49596056685463
49596056685463

2017-12-13

49596056685463

27.392

212,556

396,996

exponent	prime factors	composite factor	digits	bits*
1789373	331386679682063 177491689478873969399	58818381647563799579711452111190137	35	115.502

exponent

prime factors

composite factor

digits

bits*

1789373

331386679682063
177491689478873969399

58818381647563799579711452111190137

115.502

	GHz-Days	worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved
2016-03-16T12:34:18	alpertron	Manual testing	500000	15000000	12	-		-	-	0.101	-	-	5.055%

GHz-Days

worth

Factor
probability

date

userid

compid

stage

factor

digits

bits*

spent

saved

2016-03-16T12:34:18

alpertron

Manual testing

500000

15000000

0.101

-

-

5.055%

ECM factoring results:

Old Calculation Method

Total ECM effort:	18.258 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:	18.258 GHz-days
Estimated T-Level:	24.732

Digits	B1	Complete	FacMiss
20	11000	10.192	0.004%
25	50000	0.943	38.943%
30	250000	0.059	94.225%
35	1000000	0.003	99.722%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		264	18.19
50000	5000000	177491689478873969399	1	0.069

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2017-12-13T17:03:41	ATH	ec2-1xe	50000	5000000	177491689478873969399	67.266	1	2		1	0.069
2018-03-27T00:41:20	Chang Chia-Tche	exbpc13	50000	5000000						3	0.207
2019-09-04T12:57:34	Chang Chia-Tche	exbpc13	50000	5000000						3	0.207
2020-03-18T07:51:32	Niels_Mache_Nextcloud	SuperDry-Y	50000	5000000						3	0.207
2020-04-18T19:45:14	Oliver Kruse	Melissa	50000	5000000						3	0.207
2020-05-07T21:32:52	Greg Hogan	azure	50000	5000000						3	0.207
2020-06-15T23:27:54	nordi	sweet16	50000	5000000						3	0.207
2020-07-12T05:39:38	_p95holder_	TFL17_PRPt12pE_k	50000	5000000						3	0.207
2020-08-14T05:16:15	_p95holder_	TFL1_PRPt8pE_n	50000	5000000						3	0.207
2020-10-17T03:17:59	nordi	sweet16	50000	5000000						7	0.482
2021-01-01T22:26:49	_p95holder_	TFL15_PRPt13pE_s	50000	5000000						7	0.482
2021-01-29T12:53:56	TJAOI	Manual testing	50000	5000000						226	15.57

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-03T16:01:45

Oliver Kruse

GTX-1

331386679682063

8EB3DEF7D340DE__

2017-11-05T04:33:16

kkmrkkblmbrbk

c4.xlarge

331386679682063

8EB3DEF7D340DE__

2017-12-14T08:15:33

Luigi Morelli

AWS_01

331386679682063

177491689478873969399

070C2B33E17FCC__

2017-12-14T15:45:55

kkmrkkblmbrbk

c4.xlarge

331386679682063

177491689478873969399

070C2B33E17FCC__

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