M471041 Mersenne number exponent details

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M471041

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is 2 ⁴⁷¹⁰⁴¹ - 1

has 141798 decimal digits

takes 0.006 GHz-days to do one PRP test

Last-known PrimeNet details:

Exponent is not assigned to anyone

-unknown- primality tests remaining

	Residue	Status
L-L	-unknown-	-unknown-
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	63.0814	71.6418%	3000000	100000000	0.1415	7.2344%	63.2229	73.6933%	2.0516%
PrimeNet	2⁴⁰	0.0000	52.5000%	4500	160000	0.0002	18.6393%	0.0002	61.3537%	8.8537%
GPU72	2⁴⁴	0.0000	56.8182%	8000	260000	0.0004	13.9183%	0.0004	62.8283%	6.0102%
Difference	+23	+63.0814	+14.8236%	+2992000	+99740000	+0.1411	-6.6838%	+63.2225	+10.8650%	+10.8650%

Known prime factors (3 factors, 211.7 bits, 0.04494367% known):

Remaining cofactor is not a probable-prime

						P-1		GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
471041	5486519665131776071	19	62.251	5823823897635 3 × 5 × 388254926509	2007-08-17	5	388254926509	1.7441	361.25	674.71
471041	2299000194069964813223	22	70.961	2440339794274771 137 × 2383141 × 7474463	2014-11-27	2383141	7474463	939.23	0.0454	0.0828
471041	424774053617539910782471	24	78.491	450888620754392835 3 × 5 × 7 × 3041 × 1412093831147	2018-02-02	3041	1412093831147	245,152	1,313.9	2,454.0

4 Composite Factors:

exponent	prime factors	composite factor	digits	bits*
471041	5486519665131776071 2299000194069964813223	12613509774906631546408818992489775786833	41	133.212
471041	5486519665131776071 424774053617539910782471	2330531198410372165278835424920819564051441	43	140.742
471041	2299000194069964813223 424774053617539910782471	976555631702609894014971288134017667297414033	45	149.453
471041	5486519665131776071 2299000194069964813223 424774053617539910782471	53578916774315532795953987490366884186127992653424 97354729004343	64	211.703

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2002-06-23T00:00:00	ANONYMOUS	v4_computers	32768	3276800		-		-	-	0.004	-	-	1.739%
2002-09-14T00:00:00	ANONYMOUS	v4_computers	65536	6553600		-		-	-	0.007	-	-	2.472%
2003-04-27T00:00:00	ANONYMOUS	v4_computers	131072	13107200		-		-	-	0.014	-	-	3.332%
2014-11-27T16:13:00	alpertron	Manual testing	3000000	100000000	12		2299000194069964813223	22	70.961	0.141	0.011	0.283	7.234%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2000-04-19T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁴		-	-	0.005	-	-
2022-03-07T07:41:18	LordJulius	Manual testing	2⁵⁴	2⁵⁵		-	-	0.005	-	-
2001-03-25T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁶		-	-	0.020	-	-
2002-01-28T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁷		-	-	0.041	-	-
2004-01-07T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.082	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	12.928 GHz-days
Estimated T-Level:	26.125

Digits	B1	Curves	Complete	FacMiss
20	11000	425 / 100	4.250	1.396%
25	50000	425 / 280	1.518	21.859%
30	250000	144 / 640	0.225	79.838%

New Calculation Method

Total ECM effort:	12.928 GHz-days
Estimated T-Level:	26.125

Digits	B1	Complete	FacMiss
20	11000	23.899	0.000%
25	50000	3.028	4.840%
30	250000	0.287	75.049%
35	1000000	0.022	97.832%
40	3000000	0.001	99.860%

ECM Summary

B1	B2	factor	curves	GHz-days
		5486519665131776071	1	0.00000e+0
50000	5000000		281	3.629
250000	25000000		134	8.653
250000	25000000	424774053617539910782471	10	0.646

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2007-08-17T00:13:00	Team_Bundu	bundu1			5486519665131776071	62.251		1		1	-
2015-02-13T06:08:00	Richard B. Woods	Puttputt	50000	5000000						1	0.013
2015-05-08T10:38:00	TJAOI	Manual testing	50000	5000000						99	1.279
2016-01-29T11:41:00	TJAOI	Manual testing	50000	5000000						90	1.162
2016-07-01T10:28:21	TJAOI	Manual testing	50000	5000000						91	1.175
2018-02-02T17:06:36	TJAOI	Manual testing	250000	25000000	424774053617539910782471	78.491	10	2		10	0.646
2018-02-02T17:06:36	TJAOI	Manual testing	250000	25000000						34	2.196
2020-08-28T11:11:46	TJAOI	Manual testing	250000	25000000						100	6.458

Lucas-Lehmer results:
No L-L results for M471041

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-26T00:25:58

Oliver Kruse

Doppelherz

5486519665131776071

2299000194069964813223

164C539D5C34AFF8

2017-09-27T07:35:17

Oliver Kruse

Manual testing

5486519665131776071

2299000194069964813223

164C539D5C34AF__

2017-10-13T10:10:13

Oliver Kruse

Threadripper

164C539D5C34AF__

2017-12-16T19:25:55

ATH

xps

5486519665131776071

2299000194069964813223

164C539D5C34AF__

2018-02-02T21:20:18

MaximeG

MSI_GS63VR

5486519665131776071

2299000194069964813223

424774053617539910782471

930A1944D96848__

2018-02-03T17:29:53

trebor

Laptop

5486519665131776071

2299000194069964813223

424774053617539910782471

930A1944D96848__

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 = 3000000, B2 = 100000000 (P-1 stage 2)

B1 = 3000000 (P-1 stage 1)

B1 = 131072, B2 = 13107200 (P-1 stage 2)

B1 = 65536, B2 = 6553600 (P-1 stage 2)

B1 = 32768, B2 = 3276800 (P-1 stage 2)

B1 = 131072 (P-1 stage 1)

B1 = 65536 (P-1 stage 1)

B1 = 32768 (P-1 stage 1)

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

10¹²

10¹³

TF factor-bounds graph:

2⁶⁷

2⁵⁸

2⁵⁷

2⁵⁶

2⁵⁵

2⁵⁴

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

Last modified: 2022-03-07T07:41:18+00:00

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