M1762933 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	16.8548	68.6567%	500000	15000000	0.1015	5.0458%	16.9563	70.2382%	1.5815%
PrimeNet	2⁵⁷	0.0109	63.1579%	8000	140000	0.0012	2.8064%	0.0121	64.1918%	1.0339%
GPU72	2⁶¹	0.1742	65.5738%	8000	120000	0.0011	1.4531%	0.1754	66.0740%	0.5003%
Difference	+6	+16.6806	+3.0829%	+492000	+14880000	+0.1004	+3.5927%	+16.7809	+4.1642%	+4.1642%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

16.8548

68.6567%

500000

15000000

0.1015

5.0458%

16.9563

70.2382%

1.5815%

PrimeNet

2⁵⁷

0.0109

63.1579%

8000

140000

0.0012

2.8064%

0.0121

64.1918%

1.0339%

GPU72

2⁶¹

0.1742

65.5738%

8000

120000

0.0011

1.4531%

0.1754

66.0740%

0.5003%

Difference

+16.6806

+3.0829%

+492000

+14880000

+0.1004

+3.5927%

+16.7809

+4.1642%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1762933	38784527	8	25.209	11 11	-	1	11	2.542e-12	1.215e-7	1.601e-7
1762933	27654964537367281	17	54.618	7843453080 2³ × 3 × 5 × 19 × 139 × 24749	2015-07-21	139	24749	0.0015	0.0001	0.0002
1762933	81220240080013845975023	23	76.104	23035543630987067 246641 × 93397057387	2020-06-21	246641	93397057387	13,504	400.29	747.60

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

1762933

38784527

25.209

11
11

2.542e-12

1.215e-7

1.601e-7

1762933

27654964537367281

54.618

7843453080
2³ × 3 × 5 × 19 × 139 × 24749

2015-07-21

139

24749

0.0015

0.0001

0.0002

1762933

81220240080013845975023

76.104

23035543630987067
246641 × 93397057387

2020-06-21

246641

93397057387

13,504

400.29

747.60

exponent	prime factors	composite factor	digits	bits*
1762933	38784527 27654964537367281	1072584718783563818861087	25	79.827
1762933	38784527 81220240080013845975023	3150088594329779169592120869121	31	101.313
1762933	27654964537367281 81220240080013845975023	2246142859129239603905068818122903422463	40	130.723
1762933	38784527 27654964537367281 81220240080013845975023	87115588365755189907125447013345837106908630001	47	155.932

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2016-03-16T12:30:28	alpertron	Manual testing	500000	15000000	12	-	skipped known factor: 38784527 skipped known factor: 27654964537367281	-	-	0.101	-	-	5.046%

	Bits	Factor	GHz-Days	worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved
2014-12-04T12:09:00	TJAOI	Manual testing	2⁵⁴	2⁵⁵*	27654964537367281	54.618	17	0.000	0.202	0.000

Bits

Factor

GHz-Days

worth

date

userid

compid

from

factor

bits*

digits

spent

saved

2014-12-04T12:09:00

TJAOI

Manual testing

2⁵⁴

2⁵⁵*

27654964537367281

54.618

0.000

0.202

0.000

ECM factoring results:

Old Calculation Method

Total ECM effort:

27.308 GHz-days

Digits	B1	Curves	Complete	FacMiss
20	11000	397 / 100	3.970	1.850%
25	50000	397 / 280	1.418	24.162%

New Calculation Method

Total ECM effort:

27.308 GHz-days

Digits	B1	Complete	FacMiss
20	11000	12.806	0.000%
25	50000	1.157	31.429%
30	250000	0.071	93.121%
35	1000000	0.003	99.674%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		251	17.26
50000	5000000	81220240080013845975023	146	10.04

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2017-06-25T16:38:42	Richard B. Woods	Puttputt	50000	5000000						1	0.069
2018-03-22T19:19:21	Ismo Laitela	6600K	50000	5000000						3	0.206
2019-08-07T22:32:48	Chang Chia-Tche	exbpc13	50000	5000000						3	0.206
2020-02-29T07:14:03	Niels_Mache_Nextcloud	SuperDry-Y	50000	5000000						3	0.206
2020-03-13T02:02:56	Massimo Cappelli (ik5pwa)	maxlinux_8	50000	5000000						3	0.206
2020-04-03T08:00:25	-Anonymous-	aws-nano	50000	5000000						3	0.206
2020-05-02T03:39:15	Oliver Kruse	IOS-1	50000	5000000						3	0.206
2020-06-21T21:20:53	nordi	sweet16	50000	5000000	81220240080013845975023	76.104	146	2	8925946276510170	146	10.04
2020-10-02T07:43:10	TJAOI	Manual testing	50000	5000000						232	15.96

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-03T09:49:20

Oliver Kruse

GTX-3

38784527

27654964537367281

7EE8084F4D13E4__

2017-11-04T04:20:19

ATH

ec2-1xf

38784527

27654964537367281

7EE8084F4D13E4__

2020-06-21T23:50:13

CrypticClue

Manual testing

38784527

27654964537367281

81220240080013845975023

A6A674795B3EBE56

2020-06-23T11:42:56

Luigi Morelli

9800X

38784527

27654964537367281

81220240080013845975023

A6A674795B3EBE56

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