M1728323 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	17.1923	68.6567%	500000	15000000	0.1015	5.0338%	17.2938	70.2345%	1.5777%
PrimeNet	2⁵⁷	0.0111	63.1579%	8000	140000	0.0012	2.7959%	0.0123	64.1879%	1.0301%
GPU72	2⁶¹	0.1777	65.5738%	7000	110000	0.0010	1.3451%	0.1787	66.0368%	0.4631%
Difference	+6	+17.0146	+3.0829%	+493000	+14890000	+0.1005	+3.6887%	+17.1151	+4.1976%	+4.1976%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

17.1923

68.6567%

500000

15000000

0.1015

5.0338%

17.2938

70.2345%

1.5777%

PrimeNet

2⁵⁷

0.0111

63.1579%

8000

140000

0.0012

2.7959%

0.0123

64.1879%

1.0301%

GPU72

2⁶¹

0.1777

65.5738%

7000

110000

0.0010

1.3451%

0.1787

66.0368%

0.4631%

Difference

+17.0146

+3.0829%

+493000

+14890000

+0.1005

+3.6887%

+17.1151

+4.1976%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1728323	2770588185151	13	41.333	801525 3 × 5² × 10687	-	25	10687	2.526e-7	4.766e-5	8.552e-5
1728323	626507119632976606844447	24	79.052	181247116318239301 11 × 19 × 59 × 263 × 55887805817	2020-06-11	263	55887805817	103,054	239.52	447.36

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

1728323

2770588185151

41.333

801525
3 × 5² × 10687

10687

2.526e-7

4.766e-5

8.552e-5

1728323

626507119632976606844447

79.052

181247116318239301
11 × 19 × 59 × 263 × 55887805817

2020-06-11

263

55887805817

103,054

239.52

447.36

exponent	prime factors	composite factor	digits	bits*
1728323	2770588185151 626507119632976606844447	1735793223568109098369194458692206497	37	120.385

exponent

prime factors

composite factor

digits

bits*

1728323

2770588185151
626507119632976606844447

1735793223568109098369194458692206497

120.385

	GHz-Days	worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved
2016-03-16T12:32:42	alpertron	Manual testing	500000	15000000	12	-	skipped known factor: 2770588185151	-	-	0.101	-	-	5.034%

GHz-Days

worth

Factor
probability

date

userid

compid

stage

factor

digits

bits*

spent

saved

2016-03-16T12:32:42

alpertron

Manual testing

500000

15000000

skipped known factor: 2770588185151

0.101

-

-

5.034%

ECM factoring results:

Old Calculation Method

Total ECM effort:

21.278 GHz-days

Digits	B1	Curves	Complete	FacMiss
20	11000	310 / 100	3.100	4.435%
25	50000	310 / 280	1.107	32.985%

New Calculation Method

Total ECM effort:

21.278 GHz-days

Digits	B1	Complete	FacMiss
20	11000	10.000	0.005%
25	50000	0.904	40.503%
30	250000	0.056	94.587%
35	1000000	0.003	99.745%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		257	17.64
50000	5000000	626507119632976606844447	53	3.638

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2016-10-19T20:16:01	Richard B. Woods	Puttputt	50000	5000000						1	0.069
2018-03-14T03:32:32	Alvin Bunk	europe-west4-a	50000	5000000						3	0.206
2019-06-10T14:51:53	Chang Chia-Tche	exbpc13	50000	5000000						3	0.206
2020-02-13T14:37:21	Niels_Mache_Nextcloud	SuperDry-Y	50000	5000000						3	0.206
2020-02-21T15:11:00	Niels_Mache_Nextcloud	SuperDry-Y	50000	5000000						3	0.206
2020-02-29T13:12:35	kracker	O0	50000	5000000						3	0.206
2020-03-12T09:02:36	Niels_Mache_Nextcloud	SuperDry-Y	50000	5000000						3	0.206
2020-04-08T07:52:45	Team_Inspector	SpudBoy4	50000	5000000						3	0.206
2020-05-02T02:27:40	Greg Hogan	azure3	50000	5000000						3	0.206
2020-06-08T08:21:36	TJAOI	Manual testing	50000	5000000						232	15.92
2020-06-11T18:00:31	nordi	sweet16	50000	5000000	626507119632976606844447	79.052	53	2	166730199216302	53	3.638

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-30T15:16:27

alpertron

Manual testing

2770588185151

16A57C7EC521BD__

2017-10-19T06:47:39

Oliver Kruse

Threadripper

2770588185151

16A57C7EC521BD__

2020-06-12T20:37:10

Luigi Morelli

9800X

2770588185151

626507119632976606844447

3242107F192DCA17

2020-06-13T19:48:07

marssystems

system03

2770588185151

626507119632976606844447

3242107F192DCA17

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