M1931053 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	15.3874	68.6567%	500000	15000000	0.1015	5.1015%	15.4889	70.2557%	1.5990%
PrimeNet	2⁵⁸	0.0199	63.7931%	8000	140000	0.0012	2.4621%	0.0211	64.6846%	0.8915%
GPU72	2⁶²	0.3181	66.1290%	8000	90000	0.0010	1.1507%	0.3191	66.5188%	0.3898%
Difference	+5	+15.0693	+2.5277%	+492000	+14910000	+0.1005	+3.9508%	+15.1698	+3.7369%	+3.7369%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

15.3874

68.6567%

500000

15000000

0.1015

5.1015%

15.4889

70.2557%

1.5990%

PrimeNet

2⁵⁸

0.0199

63.7931%

8000

140000

0.0012

2.4621%

0.0211

64.6846%

0.8915%

GPU72

2⁶²

0.3181

66.1290%

8000

90000

0.0010

1.1507%

0.3191

66.5188%

0.3898%

Difference

+15.0693

+2.5277%

+492000

+14910000

+0.1005

+3.9508%

+15.1698

+3.7369%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1931053	1294779946378543	16	50.202	335252307 3 × 13 × 8596213	-	13	8596213	0.0001	0.0368	0.0688
1931053	6755591377640207	16	52.585	1749198851 61 × 28675391	2014-08-17	61	28675391	0.0005	0.1229	0.2295
1931053	139016678290804798391	21	66.914	35995044747815 5 × 1859999 × 3870437	2020-11-06	1859999	3870437	13.838	0.1549	0.2978

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

1931053

1294779946378543

50.202

335252307
3 × 13 × 8596213

8596213

0.0001

0.0368

0.0688

1931053

6755591377640207

52.585

1749198851
61 × 28675391

2014-08-17

28675391

0.0005

0.1229

0.2295

1931053

139016678290804798391

66.914

35995044747815
5 × 1859999 × 3870437

2020-11-06

1859999

3870437

13.838

0.1549

0.2978

exponent	prime factors	composite factor	digits	bits*
1931053	1294779946378543 6755591377640207	8747004241696334653754878878401	31	102.787
1931053	1294779946378543 139016678290804798391	179996007263091399607475987683324313	36	117.115
1931053	6755591377640207 139016678290804798391	939139873209543444958984341970506937	36	119.499
1931053	1294779946378543 6755591377640207 139016678290804798391	12159794746762043333730079227965273152440270094527 91	52	169.700

	GHz-Days	worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved
2016-03-16T12:40:41	alpertron	Manual testing	500000	15000000	12	-	skipped known factor: 1294779946378543	-	-	0.101	-	-	5.101%

GHz-Days

worth

Factor
probability

date

userid

compid

stage

factor

digits

bits*

spent

saved

2016-03-16T12:40:41

alpertron

Manual testing

500000

15000000

skipped known factor: 1294779946378543

0.101

-

-

5.101%

	Bits	Factor	GHz-Days	worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved
2014-08-17T11:36:00	TJAOI	Manual testing	?	?	6755591377640207	52.585	16	0.000	0.232	0.000

Bits

Factor

GHz-Days

worth

date

userid

compid

from

factor

bits*

digits

spent

saved

2014-08-17T11:36:00

TJAOI

Manual testing

6755591377640207

52.585

0.000

0.232

0.000

ECM factoring results:

Old Calculation Method

Total ECM effort:	19.346 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:	19.346 GHz-days
Estimated T-Level:	24.482

Digits	B1	Complete	FacMiss
20	11000	8.571	0.019%
25	50000	0.776	46.005%
30	250000	0.048	95.311%
35	1000000	0.002	99.779%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		34	2.363
50000	5000000	139016678290804798391	4	0.278
50000	6600000		213	16.71

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2017-12-20T10:58:04	alpertron	laptop2	50000	5000000						3	0.208
2019-02-10T02:41:13	ATH	ec2-ECMCF	50000	5000000						3	0.208
2020-11-06T10:10:30	nordi	sweet16	50000	5000000	139016678290804798391	66.914	4	2	6210968488330297	4	0.278
2021-01-15T13:13:04	_p95holder_	TFL17_PRPt12pE_k	50000	5000000						7	0.486
2021-04-11T05:52:37	_p95holder_	TFL15_PRPt13pE_s	50000	5000000						7	0.486
2021-07-22T12:09:12	Jonathan Webb	Desktop2021	50000	5000000						7	0.486
2021-10-07T04:55:29	_p95holder_	TFL15_PRPt13pE_s	50000	5000000						7	0.486
2022-02-17T11:38:42	TJAOI	Manual testing	50000	6600000						213	16.71

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-05T01:08:12

Oliver Kruse

GTX-3

1294779946378543

6755591377640207

3A1155CED6DAF4__

2017-11-10T23:44:55

kkmrkkblmbrbk

old

1294779946378543

6755591377640207

3A1155CED6DAF4__

2020-11-06T11:41:35

ATH

ec2-PRPCF

1294779946378543

6755591377640207

139016678290804798391

43662121F1433CA0

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

10⁷

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