M1805261 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	16.4596	68.6567%	500000	15000000	0.1015	5.0603%	16.5611	70.2428%	1.5861%
PrimeNet	2⁵⁷	0.0106	63.1579%	8000	150000	0.0012	2.8717%	0.0119	64.2159%	1.0580%
GPU72	2⁶¹	0.1702	65.5738%	9000	130000	0.0012	1.5553%	0.1714	66.1092%	0.5354%
Difference	+6	+16.2895	+3.0829%	+491000	+14870000	+0.1002	+3.5050%	+16.3897	+4.1336%	+4.1336%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

16.4596

68.6567%

500000

15000000

0.1015

5.0603%

16.5611

70.2428%

1.5861%

PrimeNet

2⁵⁷

0.0106

63.1579%

8000

150000

0.0012

2.8717%

0.0119

64.2159%

1.0580%

GPU72

2⁶¹

0.1702

65.5738%

9000

130000

0.0012

1.5553%

0.1714

66.1092%

0.5354%

Difference

+16.2895

+3.0829%

+491000

+14870000

+0.1002

+3.5050%

+16.3897

+4.1336%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1805261	14442089	8	23.784	4 2²	-	4	4	6.196e-13	3.146e-7	6.404e-7
1805261	893499489863	12	39.701	247471 7 × 35353	2008-07-15	7	35353	6.350e-8	0.0002	0.0003
1805261	4236500744332774871959	22	71.843	1173376244302839 3² × 1217 × 107128297663	2020-06-11	1217	107128297663	501.02	459.13	857.52

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

1805261

14442089

23.784

4
2²

6.196e-13

3.146e-7

6.404e-7

1805261

893499489863

39.701

247471
7 × 35353

2008-07-15

35353

6.350e-8

0.0002

0.0003

1805261

4236500744332774871959

71.843

1173376244302839
3² × 1217 × 107128297663

2020-06-11

1217

107128297663

501.02

459.13

857.52

exponent	prime factors	composite factor	digits	bits*
1805261	14442089 893499489863	12903999154056043807	20	63.484
1805261	14442089 4236500744332774871959	61183920798220180317795482351	29	95.627
1805261	893499489863 4236500744332774871959	3785311253865554136406591643451617	34	111.544
1805261	14442089 893499489863 4236500744332774871959	54667802021027926872302136701384519907913	41	135.328

	GHz-Days	worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved
2016-03-16T12:36:17	alpertron	Manual testing	500000	15000000	12	-	skipped known factor: 14442089 skipped known factor: 893499489863	-	-	0.101	-	-	5.060%

GHz-Days

worth

Factor
probability

date

userid

compid

stage

factor

digits

bits*

spent

saved

2016-03-16T12:36:17

alpertron

Manual testing

500000

15000000

skipped known factor: 14442089
skipped known factor: 893499489863

0.101

-

-

5.060%

	Bits	Factor	GHz-Days	worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved
2008-07-15T07:46:00	J Feitsma	Manual testing	?	?	893499489863	39.701	12	2.29276e-8	0.210	4.91272e-8

Bits

Factor

GHz-Days

worth

date

userid

compid

from

factor

bits*

digits

spent

saved

2008-07-15T07:46:00

J Feitsma

Manual testing

893499489863

39.701

2.29276e-8

0.210

4.91272e-8

ECM factoring results:

Old Calculation Method

Total ECM effort:	17.310 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:	17.310 GHz-days
Estimated T-Level:	24.482

Digits	B1	Complete	FacMiss
20	11000	8.097	0.030%
25	50000	0.732	48.105%
30	250000	0.045	95.594%
35	1000000	0.002	99.794%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		249	17.17
50000	5000000	4236500744332774871959	2	0.138

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2016-08-19T04:41:39	Richard B. Woods	Puttputt	50000	5000000						1	0.069
2018-03-31T20:38:02	Oliver Kruse	ECM-HTC	50000	5000000						3	0.207
2019-09-15T04:43:26	Chang Chia-Tche	exbpc13	50000	5000000						3	0.207
2020-04-14T11:10:21	Oliver Kruse	Melissa	50000	5000000						3	0.207
2020-05-06T03:18:51	Greg Hogan	azure2	50000	5000000						3	0.207
2020-06-11T19:21:35	nordi	sweet16	50000	5000000	4236500744332774871959	71.843	2	2	2111851597694922	2	0.138
2020-06-28T01:17:56	nordi	sweet16	50000	5000000						3	0.207
2020-07-25T06:36:15	Ahmed Azhad	c5.4xlarge.azf	50000	5000000						3	0.207
2020-09-30T20:25:13	_p95holder_	TFL17_PRPt12pE_k	50000	5000000						7	0.483
2020-11-29T06:39:36	_p95holder_	TFL17_PRPt12pE_k	50000	5000000						7	0.483
2021-01-29T12:55:47	TJAOI	Manual testing	50000	5000000						216	14.90

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-03T19:36:43

Oliver Kruse

GTX-3

14442089

893499489863

0208540B9FF1C6__

2017-11-11T03:12:45

kkmrkkblmbrbk

c4.xlarge

14442089

893499489863

0208540B9FF1C6__

2020-06-11T19:30:06

ATH

ec2-PRPCF

14442089

893499489863

4236500744332774871959

3B53D14D3632CDDD

2020-06-13T05:41:01

Team_Inspector

SpudBoy4

14442089

893499489863

4236500744332774871959

3B53D14D3632CDDD

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

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