M1838747 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	16.1599	68.6567%	500000	15000000	0.1015	5.0715%	16.2613	70.2463%	1.5896%
PrimeNet	2⁵⁷	0.0104	63.1579%	8000	150000	0.0012	2.8817%	0.0117	64.2196%	1.0617%
GPU72	2⁶¹	0.1671	65.5738%	9000	140000	0.0013	1.5961%	0.1683	66.1233%	0.5495%
Difference	+6	+15.9928	+3.0829%	+491000	+14860000	+0.1002	+3.4753%	+16.0930	+4.1230%	+4.1230%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

16.1599

68.6567%

500000

15000000

0.1015

5.0715%

16.2613

70.2463%

1.5896%

PrimeNet

2⁵⁷

0.0104

63.1579%

8000

150000

0.0012

2.8817%

0.0117

64.2196%

1.0617%

GPU72

2⁶¹

0.1671

65.5738%

9000

140000

0.0013

1.5961%

0.1683

66.1233%

0.5495%

Difference

+15.9928

+3.0829%

+491000

+14860000

+0.1002

+3.4753%

+16.0930

+4.1230%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1838747	172283238913	12	37.326	46848 2⁸ × 3 × 61	-	256	256	1.135e-8	2.014e-5	4.098e-5
1838747	573618823864601	15	49.027	155980900 2² × 5² × 37 × 42157	2008-08-26	37	42157	4.485e-5	0.0002	0.0003
1838747	8169468012184375311551	22	72.791	2221476911229325 5² × 88859076449173	2019-01-07	25	88859076449173	908.00	380,828	711,280

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

1838747

172283238913

37.326

46848
2⁸ × 3 × 61

256

1.135e-8

2.014e-5

4.098e-5

1838747

573618823864601

49.027

155980900
2² × 5² × 37 × 42157

2008-08-26

42157

4.485e-5

0.0002

0.0003

1838747

8169468012184375311551

72.791

2221476911229325
5² × 88859076449173

2019-01-07

88859076449173

908.00

380,828

711,280

exponent	prime factors	composite factor	digits	bits*
1838747	172283238913 573618823864601	98824908876859120046418713	26	86.353
1838747	172283238913 8169468012184375311551	1407462409335271926805599741584063	34	110.117
1838747	573618823864601 8169468012184375311551	4686160632748681238004766003215306151	37	121.818
1838747	172283238913 573618823864601 8169468012184375311551	807346931876536301612855716764602715791171453863	48	159.144

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2016-03-16T12:40:27	alpertron	Manual testing	500000	15000000	12	-	skipped known factor: 172283238913 skipped known factor: 573618823864601	-	-	0.101	-	-	5.071%

	Bits	Factor	GHz-Days	worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved
2008-08-26T20:20:00	ANONYMOUS	Manual testing	?	?	573618823864601	49.027	15	4.06095e-6	0.213	8.67968e-6

Bits

Factor

GHz-Days

worth

date

userid

compid

from

factor

bits*

digits

spent

saved

2008-08-26T20:20:00

ANONYMOUS

Manual testing

573618823864601

49.027

4.06095e-6

0.213

8.67968e-6

ECM factoring results:

Old Calculation Method

Total ECM effort:	19.239 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:	19.239 GHz-days
Estimated T-Level:	24.482

Digits	B1	Complete	FacMiss
20	11000	8.575	0.019%
25	50000	0.777	45.986%
30	250000	0.048	95.308%
35	1000000	0.002	99.779%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		33	2.280
50000	5000000	8169468012184375311551	3	0.207
50000	6600000		215	16.75

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2017-12-15T14:46:57	Gordon Spence	haswell	50000	5000000						3	0.207
2019-01-07T06:33:05	Chang Chia-Tche	exbpc13	50000	5000000	8169468012184375311551	72.791	3	2		3	0.207
2020-05-23T19:59:20	Chang Chia-Tche	exbpc13	50000	5000000						3	0.207
2020-06-24T19:52:48	kracker	O0	50000	5000000						3	0.207
2020-07-22T22:25:34	_p95holder_	TFL18_PRPt12pE_m	50000	5000000						3	0.207
2020-11-25T12:21:07	nordi	sweet16	50000	5000000						7	0.484
2020-11-30T08:33:41	Ondrej Vainlich	Intel_Core_i3_CAD	50000	5000000						7	0.484
2021-02-21T22:44:26	_p95holder_	TFL18_PRPt12pE_m	50000	5000000						7	0.484
2021-05-28T18:40:35	TJAOI	Manual testing	50000	6600000						215	16.75

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-04T03:23:29

Oliver Kruse

GTX-1

172283238913

573618823864601

EE70D0818814B1__

2017-11-06T12:21:24

kkmrkkblmbrbk

c4.xlarge

172283238913

573618823864601

EE70D0818814B1__

2019-01-07T13:22:15

Oliver Kruse

GTX-7

172283238913

573618823864601

8169468012184375311551

F6A7B775E28DB699

2019-01-08T10:49:56

kkmrkkblmbrbk

c5.large

172283238913

573618823864601

8169468012184375311551

F6A7B775E28DB699

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