M2932271 Mersenne number exponent details

Residue

Status

L-L

569F7AD638FB8A48

double-checked

PRP

D02898326E861D30

verified PRP

	Trial Factoring	P-1 Factoring	Combined
Limit	GHz-days	Probability	B1	B2	GHz-days	Probability	GHz-days	Probability	Prob over default TF
Actual	2⁶⁸	20.3272	67.6471%	1000000	20000000	0.2512	5.5399%	20.5784	69.4394%	1.7923%
PrimeNet	2⁵⁹	0.0262	62.7119%	13000	260000	0.0033	3.0703%	0.0295	63.8567%	1.1449%
GPU72	2⁶³	0.5443	65.0794%	17000	300000	0.0040	1.9454%	0.5483	65.7587%	0.6794%
Difference	+5	+19.7829	+2.5677%	+983000	+19700000	+0.2472	+3.5945%	+20.0301	+3.6807%	+3.6807%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁸

20.3272

67.6471%

1000000

20000000

0.2512

5.5399%

20.5784

69.4394%

1.7923%

PrimeNet

2⁵⁹

0.0262

62.7119%

13000

260000

0.0033

3.0703%

0.0295

63.8567%

1.1449%

GPU72

2⁶³

0.5443

65.0794%

17000

300000

0.0040

1.9454%

0.5483

65.7587%

0.6794%

Difference

+19.7829

+2.5677%

+983000

+19700000

+0.2472

+3.5945%

+20.0301

+3.6807%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2932271	545172377810228677246009	24	78.851	92960776444303524 2² × 3 × 17 × 313 × 709 × 2053425743	2021-01-08	709	2053425743	35,084	13.807	25.787

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

2932271

545172377810228677246009

78.851

92960776444303524
2² × 3 × 17 × 313 × 709 × 2053425743

2021-01-08

709

2053425743

35,084

13.807

25.787

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2003-12-13T00:00:00	ANONYMOUS	v4_computers	2048	204800		-		-	-	0.002	-	-	0.246%
2003-12-23T00:00:00	Team Prime Rib	v4_computers	10000	10000		-		-	-	0.001	-	-	0.145%
2010-11-09T20:59:00	markr	tiny	105000	2283750		-		-	-	0.028	-	-	2.584%
2015-04-29T15:00:00	VictordeHollander	Manual testing	1000000	20000000		-		-	-	0.251	-	-	5.540%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1998-04-11T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁹		-	-	0.026	-	-
2016-02-23T16:29:24	Mark Rose	Manual testing	2⁵⁹	2⁶⁰		-	-	0.026	-	-
2009-02-13T01:07:00	Sturle Sunde	golli.ifi	2⁶⁰	2⁶¹		-	-	0.052	-	-
2011-12-19T06:20:00	Sebastian Hornbostel	Manual testing	2⁶¹	2⁶²		-	-	0.105	-	-
2013-01-10T21:10:00	dbaugh	Manual testing	2⁶²	2⁶³		-	-	0.335	-	-
2015-04-25T17:16:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.670	-	-
2015-04-25T17:16:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.274	-	-
2016-02-23T09:49:05	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	2.548	-	-
2017-11-23T20:18:50	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	5.097	-	-
2018-12-20T02:16:15	chuenkit	Manual testing	2⁶⁷	2⁶⁸		-	-	10.19	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	5.553 GHz-days
Estimated T-Level:	2.400

Digits	B1	Curves	Complete	FacMiss
20	11000	48 / 100	0.480	61.729%
25	50000	48 / 280	0.171	84.220%

New Calculation Method

Total ECM effort:	5.553 GHz-days
Estimated T-Level:	2.400

Digits	B1	Complete	FacMiss
20	11000	1.846	15.784%
25	50000	0.171	84.297%
30	250000	0.011	98.928%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		46	5.321
50000	5000000	545172377810228677246009	2	0.231

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-04-04T03:05:00	Newro	home	50000	5000000						3	0.347
2011-04-12T06:12:00	rduerr	r40_16	50000	5000000						3	0.347
2013-06-20T06:12:00	Bruce	fx6840-21	50000	5000000						3	0.347
2015-12-28T06:30:35	Bruce	Desk7	50000	5000000						3	0.347
2017-05-25T11:43:51	Conductor	NataW	50000	5000000						3	0.347
2019-08-23T13:10:26	Idgo	Pentium_Desktop	50000	5000000						3	0.347
2020-09-03T07:58:21	Nesowa	6700T	50000	5000000						7	0.810
2020-10-05T09:27:15	daveward2005	Davy	50000	5000000						7	0.810
2020-10-31T11:43:06	daveward2005	Dave2	50000	5000000						7	0.810
2020-12-06T03:00:57	Zenzoma	AM3700X_1	50000	5000000						7	0.810
2021-01-08T01:40:14	Zenzoma	AMD3970X	50000	5000000	545172377810228677246009	78.851	2	2	8507948042403668	2	0.231

date	userid	compid	res64	spent (GHz-days)
1998-04-11T00:00:00	ANONYMOUS	v4_computers	569F7AD638FB8A48	0.250
1999-10-21T00:00:00	ANONYMOUS	v4_computers	569F7AD638FB8A48	0.250

date

userid

compid

res64

spent (GHz-days)

1998-04-11T00:00:00

ANONYMOUS

v4_computers

569F7AD638FB8A48

0.250

1999-10-21T00:00:00

ANONYMOUS

v4_computers

569F7AD638FB8A48

0.250

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 = 1000000, B2 = 20000000 (P-1 stage 2)

B1 = 1000000 (P-1 stage 1)

B1 = 105000, B2 = 2283750 (P-1 stage 2)

B1 = 105000 (P-1 stage 1)

B1 = 2048, B2 = 204800 (P-1 stage 2)

B1 = 10000 (P-1 stage 1)

B1 = 2048 (P-1 stage 1)

10¹

10²

10³

10⁴

10⁵

10⁶

10¹

10²

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