M1732273 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	17.1531	68.6567%	500000	15000000	0.1015	5.0352%	17.2546	70.2349%	1.5782%
PrimeNet	2⁵⁷	0.0111	63.1579%	8000	140000	0.0012	2.7971%	0.0123	64.1884%	1.0305%
GPU72	2⁶¹	0.1773	65.5738%	7000	110000	0.0010	1.3457%	0.1783	66.0370%	0.4633%
Difference	+6	+16.9758	+3.0829%	+493000	+14890000	+0.1005	+3.6894%	+17.0763	+4.1979%	+4.1979%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

17.1531

68.6567%

500000

15000000

0.1015

5.0352%

17.2546

70.2349%

1.5782%

PrimeNet

2⁵⁷

0.0111

63.1579%

8000

140000

0.0012

2.7971%

0.0123

64.1884%

1.0305%

GPU72

2⁶¹

0.1773

65.5738%

7000

110000

0.0010

1.3457%

0.1783

66.0370%

0.4633%

Difference

+16.9758

+3.0829%

+493000

+14890000

+0.1005

+3.6894%

+17.0763

+4.1979%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1732273	10393639	8	23.309	3 3	-	1	3	6.455e-13	8.723e-8	1.601e-7
1732273	453593429989144904639	21	68.620	130924349103503 29 × 31 × 4903 × 29702899	2020-05-04	4903	29702899	36.373	0.1277	0.2378

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

1732273

10393639

23.309

3
3

6.455e-13

8.723e-8

1.601e-7

1732273

453593429989144904639

68.620

130924349103503
29 × 31 × 4903 × 29702899

2020-05-04

4903

29702899

36.373

0.1277

0.2378

exponent	prime factors	composite factor	digits	bits*
1732273	10393639 453593429989144904639	4714486364078946057507191321	28	91.929

exponent

prime factors

composite factor

digits

bits*

1732273

10393639
453593429989144904639

4714486364078946057507191321

91.929

	GHz-Days	worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved
2016-03-16T12:33:15	alpertron	Manual testing	500000	15000000	12	-	skipped known factor: 10393639	-	-	0.101	-	-	5.035%

GHz-Days

worth

Factor
probability

date

userid

compid

stage

factor

digits

bits*

spent

saved

2016-03-16T12:33:15

alpertron

Manual testing

500000

15000000

skipped known factor: 10393639

0.101

-

-

5.035%

ECM factoring results:

Old Calculation Method

Total ECM effort:	17.713 GHz-days
Estimated T-Level:	24.607

Digits	B1	Curves	Complete	FacMiss
20	11000	258 / 100	2.580	7.480%
25	50000	258 / 280	0.921	39.729%

New Calculation Method

Total ECM effort:	17.713 GHz-days
Estimated T-Level:	24.607

Digits	B1	Complete	FacMiss
20	11000	8.323	0.024%
25	50000	0.752	47.133%
30	250000	0.046	95.474%
35	1000000	0.002	99.788%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		257	17.64
50000	5000000	453593429989144904639	1	0.069

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2016-11-20T21:29:08	Richard B. Woods	Puttputt	50000	5000000						1	0.069
2018-03-15T13:30:20	Ismo Laitela	6600K	50000	5000000						3	0.206
2019-06-16T19:56:51	Chang Chia-Tche	exbpc13	50000	5000000						3	0.206
2020-02-15T14:47:16	Niels_Mache_Nextcloud	SuperDry-Y	50000	5000000						3	0.206
2020-02-23T12:00:04	Niels_Mache_Nextcloud	SuperDry-Y	50000	5000000						3	0.206
2020-03-03T01:07:31	Niels_Mache_Nextcloud	SuperDry-Y	50000	5000000						3	0.206
2020-03-15T09:04:31	Niels_Mache_Nextcloud	SuperDry-Y	50000	5000000						3	0.206
2020-04-12T04:22:13	Oliver Kruse	Melissa	50000	5000000						3	0.206
2020-05-04T19:03:33	Chang Chia-Tche	exbpc13	50000	5000000	453593429989144904639	68.620	1	2		1	0.069
2020-05-09T11:53:42	Greg Hogan	azure2	50000	5000000						3	0.206
2020-05-25T09:38:33	TJAOI	Manual testing	50000	5000000						232	15.93

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-30T15:16:17

alpertron

Manual testing

10393639

C8A913B129C58C__

2017-10-19T08:43:21

Oliver Kruse

Threadripper

10393639

C8A913B129C58C__

2020-05-07T13:22:16

mnd9

mnd

10393639

453593429989144904639

A04CA0F82459703C

2020-05-08T10:10:09

Sébastien Broucke

130302

10393639

453593429989144904639

A04CA0F82459703C

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