M1802897 Mersenne number exponent details

Residue

Status

L-L

FD274C82B20F0C1E

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	16.4812	68.6567%	2780000	91760000	0.6000	8.1173%	17.0812	71.2009%	2.5442%
PrimeNet	2⁵⁷	0.0106	63.1579%	8000	150000	0.0012	2.8710%	0.0119	64.2156%	1.0577%
GPU72	2⁶¹	0.1704	65.5738%	9000	130000	0.0012	1.5549%	0.1716	66.1091%	0.5353%
Difference	+6	+16.3108	+3.0829%	+2771000	+91630000	+0.5988	+6.5624%	+16.9096	+5.0919%	+5.0919%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

16.4812

68.6567%

2780000

91760000

0.6000

8.1173%

17.0812

71.2009%

2.5442%

PrimeNet

2⁵⁷

0.0106

63.1579%

8000

150000

0.0012

2.8710%

0.0119

64.2156%

1.0577%

GPU72

2⁶¹

0.1704

65.5738%

9000

130000

0.0012

1.5549%

0.1716

66.1091%

0.5353%

Difference

+16.3108

+3.0829%

+2771000

+91630000

+0.5988

+6.5624%

+16.9096

+5.0919%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1802897	972875739504258667942399	24	79.687	269809018347764367 3² × 47 × 101429 × 6288599701	2017-11-14	101429	6288599701	69,188	26.959	50.338

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

1802897

972875739504258667942399

79.687

269809018347764367
3² × 47 × 101429 × 6288599701

2017-11-14

101429

6288599701

69,188

26.959

50.338

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2003-09-21T00:00:00	Team Prime Rib	v4_computers	25000	387500		-		-	-	0.004	-	-	1.199%
2011-02-07T12:38:00	Carsten Kossendey	leela	100000	1650000		-		-	-	0.015	-	-	2.477%
2014-05-12T10:21:00	Jocelyn Larouche	Manual testing	135601	135601		-		-	-	0.011	-	-	1.060%
2014-09-20T22:31:00	Jocelyn Larouche	Manual testing	171202	171202		-		-	-	0.013	-	-	1.201%
2015-04-30T18:45:00	mikr	MSI	2780000	91760000		-		-	-	0.600	-	-	8.117%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2003-01-25T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.021	-	-
2016-02-23T16:28:52	Mark Rose	Manual testing	2⁵⁸	2⁶⁰		-	-	0.064	-	-
2010-04-11T18:26:00	Architects Cubed	m1_tt	2⁶⁰	2⁶¹		-	-	0.085	-	-
2016-02-23T16:28:52	Mark Rose	Manual testing	2⁶¹	2⁶²		-	-	0.170	-	-
2010-12-13T03:33:00	GrunwalderGIMP	Manual testing	2¹	2⁶³		-	-	0.885	-	-
2016-02-23T16:28:52	Mark Rose	Manual testing	2⁶²	2⁶³		-	-	0.544	-	-
2015-04-20T21:13:00	snme2pm1	Manual testing	2⁶³	2⁶⁴		-	-	1.089	-	-
2015-04-20T21:13:00	snme2pm1	Manual testing	2⁶⁴	2⁶⁵		-	-	2.072	-	-
2015-08-31T08:30:00	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	4.145	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	17.307 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:	17.307 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		248	17.10
50000	5000000	972875739504258667942399	3	0.207

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2008-09-11T05:34:00	Scott Kurowski	UW1	50000	5000000						3	0.207
2009-07-16T04:49:00	SubPrime	stor	50000	5000000						3	0.207
2010-10-12T22:26:00	Lupo	yorick	50000	5000000						3	0.207
2012-03-27T14:08:00	OS1	L3	50000	5000000						3	0.207
2013-07-13T07:21:00	Sara	Sara	50000	5000000						3	0.207
2014-03-24T08:50:00	Chang Chia-Tche	exbpc13	50000	5000000						3	0.207
2014-07-04T10:13:00	mikr	MSI	50000	5000000						12	0.827
2016-05-19T04:32:43	Bruce	DESK3	50000	5000000						3	0.207
2016-09-07T09:45:30	Chang Chia-Tche	exbpc13	50000	5000000						3	0.207
2016-10-25T11:53:39	Bruce	DESK3	50000	5000000						3	0.207
2016-12-28T18:17:00	Bruce	DESK3	50000	5000000						3	0.207
2017-04-20T23:54:58	ANONYMOUS	Worker	50000	5000000						3	0.207
2017-11-14T11:38:42	Bruce	DESK3	50000	5000000	972875739504258667942399	79.687	3	2		3	0.207
2021-01-29T12:54:53	TJAOI	Manual testing	50000	5000000						203	14.00

date	userid	compid	res64	spent (GHz-days)
1999-03-01T00:00:00	dtlgc	v4_computers	FD274C82B20F0C1E	0.098
2002-10-19T00:00:00	dtlgc	v4_computers	FD274C82B20F0C1E	0.098
2015-06-27T00:55:00	MadPoo	Manual testing	FD274C82B20F0C1E	0.098

date

userid

compid

res64

spent (GHz-days)

1999-03-01T00:00:00

dtlgc

v4_computers

FD274C82B20F0C1E

0.098

2002-10-19T00:00:00

dtlgc

v4_computers

FD274C82B20F0C1E

0.098

2015-06-27T00:55:00

MadPoo

Manual testing

FD274C82B20F0C1E

0.098

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 = 1650000 (P-1 stage 2)

B1 = 171202 (P-1 stage 1)

B1 = 135601 (P-1 stage 1)

B1 = 100000 (P-1 stage 1)

B1 = 25000, B2 = 387500 (P-1 stage 2)

B1 = 25000 (P-1 stage 1)

10³

10⁴

10⁵

10⁶

10⁷

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

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