M1825781 Mersenne number exponent details

Residue

Status

L-L

F50FBB1B5FD6A1BB

double-checked

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	16.2746	68.6567%	500000	15000000	0.1015	5.0672%	16.3761	70.2449%	1.5882%
PrimeNet	2⁵⁷	0.0105	63.1579%	8000	150000	0.0012	2.8779%	0.0118	64.2182%	1.0603%
GPU72	2⁶¹	0.1682	65.5738%	9000	140000	0.0013	1.5938%	0.1695	66.1225%	0.5487%
Difference	+6	+16.1064	+3.0829%	+491000	+14860000	+0.1002	+3.4733%	+16.2066	+4.1225%	+4.1225%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

16.2746

68.6567%

500000

15000000

0.1015

5.0672%

16.3761

70.2449%

1.5882%

PrimeNet

2⁵⁷

0.0105

63.1579%

8000

150000

0.0012

2.8779%

0.0118

64.2182%

1.0603%

GPU72

2⁶¹

0.1682

65.5738%

9000

140000

0.0013

1.5938%

0.1695

66.1225%

0.5487%

Difference

+16.1064

+3.0829%

+491000

+14860000

+0.1002

+3.4733%

+16.2066

+4.1225%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1825781	1056901939637146327007	22	69.840	289438311505363 289438311505363	2020-06-16	1	289438311505363	86.410	1,240,460	2,316,834
1825781	2811454102827449665559	22	71.252	769931909365759 7 × 2333 × 47145423389	2011-03-06	2333	47145423389	300.35	202.05	377.38

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

1825781

1056901939637146327007

69.840

289438311505363
289438311505363

2020-06-16

289438311505363

86.410

1,240,460

2,316,834

1825781

2811454102827449665559

71.252

769931909365759
7 × 2333 × 47145423389

2011-03-06

2333

47145423389

300.35

202.05

377.38

exponent	prime factors	composite factor	digits	bits*
1825781	1056901939637146327007 2811454102827449665559	2971431294479144589119478666809087399451913	43	141.092

exponent

prime factors

composite factor

digits

bits*

1825781

1056901939637146327007
2811454102827449665559

2971431294479144589119478666809087399451913

141.092

	GHz-Days	worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved
2016-03-16T12:38:49	alpertron	Manual testing	500000	15000000	12	-		-	-	0.101	-	-	5.067%

GHz-Days

worth

Factor
probability

date

userid

compid

stage

factor

digits

bits*

spent

saved

2016-03-16T12:38:49

alpertron

Manual testing

500000

15000000

0.101

-

-

5.067%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2003-01-16T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.021	-	-
2022-03-08T23:06:28	LordJulius	Manual testing	2⁵⁸	2⁶⁰		-	-	0.063	-	-
2022-03-09T03:44:03	LordJulius	Manual testing	2¹	2⁶⁰		-	-	0.084	-	-
2010-04-10T15:57:00	Architects Cubed	Manual testing	2⁶⁰	2⁶¹		-	-	0.084	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	20.207 GHz-days
Estimated T-Level:	24.714

Digits	B1	Curves	Complete	FacMiss
20	11000	264 / 100	2.640	7.042%
25	50000	264 / 280	0.943	38.886%

New Calculation Method

Total ECM effort:	20.207 GHz-days
Estimated T-Level:	24.714

Digits	B1	Complete	FacMiss
20	11000	9.017	0.012%
25	50000	0.817	44.183%
30	250000	0.051	95.072%
35	1000000	0.002	99.768%

ECM Summary

B1	B2	factor	curves	GHz-days
		2811454102827449665559	1	0.00000e+0
50000	5000000		36	2.486
50000	5000000	1056901939637146327007	3	0.207
50000	6600000		225	17.51

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2008-10-02T23:02:00	Scott Kurowski	UW4	50000	5000000						3	0.207
2009-07-18T09:51:00	SubPrime	abd0	50000	5000000						3	0.207
2011-03-06T22:36:00	Lupo	yorick			2811454102827449665559	71.252		1		1	-
2020-05-08T01:41:07	Greg Hogan	azure2	50000	5000000						3	0.207
2020-06-16T06:55:11	nordi	sweet16	50000	5000000	1056901939637146327007	69.840	3	2	7165436259251224	3	0.207
2020-07-12T10:57:12	_p95holder_	TFL1_PRPt8pE_n	50000	5000000						3	0.207
2020-08-14T20:36:26	Chang Chia-Tche	exbpc13	50000	5000000						3	0.207
2020-10-17T03:57:29	J.R. Allen	lapacer	50000	5000000						7	0.483
2021-01-03T07:58:57	_p95holder_	TFL15_PRPt13pE_s	50000	5000000						7	0.483
2021-03-31T00:50:43	_p95holder_	TFL15_PRPt13pE_s	50000	5000000						7	0.483
2021-04-09T16:12:14	TJAOI	Manual testing	50000	6600000						225	17.51

date	userid	compid	res64	spent (GHz-days)
1998-12-06T00:00:00	ANONYMOUS	v4_computers	F50FBB1B5FD6A1BB	0.099
1998-12-21T00:00:00	ANONYMOUS	v4_computers	F50FBB1B5FD6A1BB	0.099

date

userid

compid

res64

spent (GHz-days)

1998-12-06T00:00:00

ANONYMOUS

v4_computers

F50FBB1B5FD6A1BB

0.099

1998-12-21T00:00:00

ANONYMOUS

v4_computers

F50FBB1B5FD6A1BB

0.099

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-04T00:31:09

Oliver Kruse

GTX-0

2811454102827449665559

FAD08C7138FF0F__

2017-11-06T02:35:21

kkmrkkblmbrbk

c4.xlarge

2811454102827449665559

FAD08C7138FF0F__

2020-06-17T02:48:18

CrypticClue

cruncher

1056901939637146327007

2811454102827449665559

95B0467285181834

2020-06-17T03:07:10

ATH

ec2-PRPCFDC

1056901939637146327007

2811454102827449665559

95B0467285181834

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

10¹⁵

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