M1858201 Mersenne number exponent details

Residue

Status

L-L

C44A1949A9B4C56A

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	15.9907	68.6567%	2780000	91760000	0.6000	8.1416%	16.5907	71.2086%	2.5518%
PrimeNet	2⁵⁷	0.0103	63.1579%	9000	160000	0.0014	3.0256%	0.0117	64.2726%	1.1147%
GPU72	2⁶¹	0.1653	65.5738%	9000	150000	0.0013	1.6324%	0.1666	66.1358%	0.5620%
Difference	+6	+15.8254	+3.0829%	+2771000	+91610000	+0.5987	+6.5092%	+16.4241	+5.0728%	+5.0728%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

15.9907

68.6567%

2780000

91760000

0.6000

8.1416%

16.5907

71.2086%

2.5518%

PrimeNet

2⁵⁷

0.0103

63.1579%

9000

160000

0.0014

3.0256%

0.0117

64.2726%

1.1147%

GPU72

2⁶¹

0.1653

65.5738%

9000

150000

0.0013

1.6324%

0.1666

66.1358%

0.5620%

Difference

+15.8254

+3.0829%

+2771000

+91610000

+0.5987

+6.5092%

+16.4241

+5.0728%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1858201	37719556559049069584464943	26	84.964	10149482364676660271 7 × 103 × 17327 × 812428692913	2017-01-22	17327	812428692913	3,811,128	3,481.9	6,503.2

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

1858201

37719556559049069584464943

84.964

10149482364676660271
7 × 103 × 17327 × 812428692913

2017-01-22

17327

812428692913

3,811,128

3,481.9

6,503.2

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2011-02-08T05:50:00	Carsten Kossendey	leela	100000	1725000		-		-	-	0.015	-	-	2.515%
2014-05-26T23:57:00	Jocelyn Larouche	Manual testing	134541	134541		-		-	-	0.011	-	-	1.061%
2014-09-29T22:04:00	Jocelyn Larouche	Manual testing	169082	169082		-		-	-	0.013	-	-	1.199%
2015-07-29T00:49:00	mikr	MSI	2780000	91760000		-		-	-	0.600	-	-	8.142%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2003-01-09T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.021	-	-
2016-02-23T16:28:55	Mark Rose	Manual testing	2⁵⁸	2⁶⁰		-	-	0.062	-	-
2010-04-13T12:48:00	Architects Cubed	a3_bu2	2⁶⁰	2⁶¹		-	-	0.083	-	-
2016-02-23T16:28:55	Mark Rose	Manual testing	2⁶¹	2⁶²		-	-	0.165	-	-
2011-01-21T16:11:00	GrunwalderGIMP	Manual testing	2¹	2⁶³		-	-	0.859	-	-
2016-02-23T16:28:55	Mark Rose	Manual testing	2⁶²	2⁶³		-	-	0.528	-	-
2015-05-06T21:11:00	snme2pm1	Manual testing	2⁶³	2⁶⁴		-	-	1.057	-	-
2015-05-06T21:11:00	snme2pm1	Manual testing	2⁶⁴	2⁶⁵		-	-	2.011	-	-
2015-09-09T11:47:00	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	4.021	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	19.221 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:	19.221 GHz-days
Estimated T-Level:	24.482

Digits	B1	Complete	FacMiss
20	11000	8.564	0.019%
25	50000	0.776	46.034%
30	250000	0.048	95.315%
35	1000000	0.002	99.780%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		39	2.698
50000	5000000	37719556559049069584464943	2	0.138
50000	6600000		210	16.38

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2008-10-22T21:10:00	ANONYMOUS	bps25	50000	5000000						3	0.208
2009-07-20T09:50:00	James Hintz	03_071509	50000	5000000						3	0.208
2011-02-10T21:22:00	James Hintz	ryan	50000	5000000						3	0.208
2012-10-15T10:24:00	Donna Noble	i3-2100t	50000	5000000						3	0.208
2013-09-25T18:03:00	Sara	Sara	50000	5000000						3	0.208
2014-06-07T05:30:00	Chang Chia-Tche	exbpc13	50000	5000000						3	0.208
2015-01-16T21:46:00	mikr	MSI	50000	5000000						12	0.830
2016-06-13T10:35:16	ANONYMOUS	desktop	50000	5000000						3	0.208
2016-09-18T14:20:23	Bruce	DESK3	50000	5000000						3	0.208
2016-11-25T02:36:31	Chang Chia-Tche	exbpc13	50000	5000000						3	0.208
2017-01-22T08:22:08	Bruce	DESK3	50000	5000000	37719556559049069584464943	84.964	2	2		2	0.138
2021-07-23T11:17:46	TJAOI	Manual testing	50000	6600000						210	16.38

date	userid	compid	res64	spent (GHz-days)
1998-12-21T00:00:00	garyfu	v4_computers	C44A1949A9B4C56A	0.101
2015-06-27T00:56:00	MadPoo	Manual testing	C44A1949A9B4C56A	0.101

date

userid

compid

res64

spent (GHz-days)

1998-12-21T00:00:00

garyfu

v4_computers

C44A1949A9B4C56A

0.101

2015-06-27T00:56:00

MadPoo

Manual testing

C44A1949A9B4C56A

0.101

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 = 2780000, B2 = 91760000 (P-1 stage 2)

B1 = 2780000 (P-1 stage 1)

B1 = 100000, B2 = 1725000 (P-1 stage 2)

B1 = 169082 (P-1 stage 1)

B1 = 134541 (P-1 stage 1)

B1 = 100000 (P-1 stage 1)

10³

10⁴

10⁵

10⁶

10⁷

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