M1848877 Mersenne number exponent details

Residue

Status

L-L

F440F27B3770E8A9

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	16.0713	68.6567%	500000	2835864570	12.1910	10.3831%	28.2623	71.9111%	3.2544%
PrimeNet	2⁵⁷	0.0104	63.1579%	9000	160000	0.0014	3.0228%	0.0117	64.2715%	1.1136%
GPU72	2⁶¹	0.1661	65.5738%	9000	150000	0.0013	1.6308%	0.1675	66.1352%	0.5614%
Difference	+6	+15.9052	+3.0829%	+491000	+2835714570	+12.1897	+8.7523%	+28.0949	+5.7759%	+5.7759%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

16.0713

68.6567%

500000

2835864570

12.1910

10.3831%

28.2623

71.9111%

3.2544%

PrimeNet

2⁵⁷

0.0104

63.1579%

9000

160000

0.0014

3.0228%

0.0117

64.2715%

1.1136%

GPU72

2⁶¹

0.1661

65.5738%

9000

150000

0.0013

1.6308%

0.1675

66.1352%

0.5614%

Difference

+15.9052

+3.0829%

+491000

+2835714570

+12.1897

+8.7523%

+28.0949

+5.7759%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1848877	247404842439955788584561	24	77.711	66906787860943640 2³ × 5 × 17 × 98392335089623	2020-12-01	17	98392335089623	32,537	421,685	787,590
1848877	287592412994476988653930061119	30	97.860	77774890648344099865467 3 × 23 × 38453 × 35436481 × 827198051	2011-01-26	35436481	827198051	3.257e+10	6.1808	6.6214

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

1848877

247404842439955788584561

77.711

66906787860943640
2³ × 5 × 17 × 98392335089623

2020-12-01

98392335089623

32,537

421,685

787,590

1848877

287592412994476988653930061119

97.860

77774890648344099865467
3 × 23 × 38453 × 35436481 × 827198051

2011-01-26

35436481

827198051

3.257e+10

6.1808

6.6214

exponent	prime factors	composite factor	digits	bits*
1848877	247404842439955788584561 287592412994476988653930061119	71151755623825273100483231173767860499027817229783 759	53	175.571

exponent

prime factors

composite factor

digits

bits*

1848877

247404842439955788584561
287592412994476988653930061119

71151755623825273100483231173767860499027817229783
759

175.571

	GHz-Days	worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved
2022-04-11T18:51:32	Lisander Viaene	Desktop	500000	2835864570		-		-	-	12.19	-	-	10.383%

GHz-Days

worth

Factor
probability

date

userid

compid

stage

factor

digits

bits*

spent

saved

2022-04-11T18:51:32

Lisander Viaene

Desktop

500000

2835864570

12.19

-

-

10.383%

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	-	-
2010-04-08T13:19:00	Architects Cubed	Manual testing	2⁶⁰	2⁶¹		-	-	0.083	-	-
2011-01-21T16:11:00	GrunwalderGIMP	Manual testing	2¹	2⁶³		-	-	0.863	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	19.669 GHz-days
Estimated T-Level:	24.571

Digits	B1	Curves	Complete	FacMiss
20	11000	256 / 100	2.560	7.631%
25	50000	256 / 280	0.914	40.015%

New Calculation Method

Total ECM effort:	19.669 GHz-days
Estimated T-Level:	24.571

Digits	B1	Complete	FacMiss
20	11000	8.754	0.016%
25	50000	0.793	45.245%
30	250000	0.049	95.212%
35	1000000	0.002	99.775%

ECM Summary

B1	B2	factor	curves	GHz-days
		287592412994476988653930061119	1	0.00000e+0
50000	5000000		26	1.798
50000	5000000	247404842439955788584561	7	0.484
50000	6600000		223	17.39

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2008-10-17T16:01:00	paulie	iMac3.4	50000	5000000						3	0.207
2009-07-19T08:38:00	James Hintz	14_071509	50000	5000000						3	0.207
2011-01-26T06:27:00	Lupo	yorick			287592412994476988653930061119	97.860		1		1	-
2020-06-29T04:21:52	nordi	sweet16	50000	5000000						3	0.207
2020-07-25T20:01:11	argusdusty	Argus-PC	50000	5000000						3	0.207
2020-10-02T19:18:46	_p95holder_	TFL17_PRPt12pE_k	50000	5000000						7	0.484
2020-12-01T06:40:07	nordi	sweet16	50000	5000000	247404842439955788584561	77.711	7	2	2846185898770857	7	0.484
2021-04-06T08:09:42	_p95holder_	TFL15_PRPt13pE_s	50000	5000000						7	0.484
2021-06-04T15:58:00	TJAOI	Manual testing	50000	6600000						223	17.39

date	userid	compid	res64	spent (GHz-days)
1998-12-21T00:00:00	ANONYMOUS	v4_computers	F440F27B3770E8A9	0.100

date

userid

compid

res64

spent (GHz-days)

1998-12-21T00:00:00

ANONYMOUS

v4_computers

F440F27B3770E8A9

0.100

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-04T05:42:32

Oliver Kruse

GTX-1

287592412994476988653930061119

6B4F63C80447A3__

2017-11-06T21:37:02

ATH

ec2-1xf

287592412994476988653930061119

6B4F63C80447A3__

2020-12-04T09:42:01

Jinyuan Wang

Manual testing

247404842439955788584561

287592412994476988653930061119

19B15F6E5544FE__

2020-12-06T05:38:24

roemer2201

ws-rebentrost-o

247404842439955788584561

287592412994476988653930061119

19B15F6E5544FEDA

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 = 2835864570 (P-1 stage 2)

B1 = 500000 (P-1 stage 1)

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

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