M506171 Mersenne number exponent details

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M506171

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is 2 ⁵⁰⁶¹⁷¹ - 1

has 152373 decimal digits

takes 0.007 GHz-days to do one PRP test

Last-known PrimeNet details:

Exponent is not assigned to anyone

0 primality tests remaining

	Residue	Status
L-L	B0BA348B550008__	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	58.7033	71.6418%	10000000	830000000	1.1562	10.7301%	59.8595	74.6846%	3.0429%
PrimeNet	2⁴⁰	0.0000	52.5000%	5000	170000	0.0003	19.1283%	0.0003	61.5859%	9.0859%
GPU72	2⁴⁴	0.0000	56.8182%	9000	280000	0.0005	14.3785%	0.0005	63.0271%	6.2089%
Difference	+23	+58.7033	+14.8236%	+9991000	+829720000	+1.1557	-3.6485%	+59.8590	+11.6576%	+11.6576%

Known prime factors (1 factor, 75.6 bits, 0.01493199% 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
506171	56528943437083617060023	23	75.581	55839769007987041 7 × 11 × 17 × 123677 × 344917337	2008-01-11	123677	344917337	28,471	0.3998	0.7422

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2000-12-07T00:00:00	Alex Kruppa	v4_computers	100000	4000000		-		-	-	0.007	-	-	2.502%
2002-06-23T00:00:00	ANONYMOUS	v4_computers	32768	3276800		-		-	-	0.004	-	-	1.762%
2002-08-31T00:00:00	ANONYMOUS	v4_computers	65536	6553600		-		-	-	0.009	-	-	2.500%
2003-04-27T00:00:00	ANONYMOUS	v4_computers	131072	13107200		-		-	-	0.018	-	-	3.366%
2016-03-16T12:40:45	alpertron	Manual testing	1500000	50000000	12	-		-	-	0.088	-	-	6.107%
2021-05-18T17:43:55	gLauss	Manual testing	10000000	830000000		-	skipped known factor: 56528943437083617060023	-	-	1.156	-	-	10.730%

P+1 Factoring results:

date	userid	compid	b1	b2	start		factor	Smooth	digits	bits*	ghz-days
2021-05-18T17:43:55	gLauss	Manual testing	5000000	365000000	2	7			-	-	0.458

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2000-03-01T00:00:00	ANONYMOUS	v4_computers	2⁵³	2⁵⁴		-	-	0.002	-	-
2022-03-07T07:41:58	LordJulius	Manual testing	2⁵⁴	2⁵⁵		-	-	0.005	-	-
2001-04-01T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁶		-	-	0.019	-	-
2001-12-22T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁷		-	-	0.038	-	-
2003-12-13T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.076	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	16.049 GHz-days
Estimated T-Level:	26.125

Digits	B1	Curves	Complete	FacMiss
20	11000	423 / 100	4.230	1.425%
25	50000	423 / 280	1.511	22.016%
30	250000	144 / 640	0.225	79.838%

New Calculation Method

Total ECM effort:	16.049 GHz-days
Estimated T-Level:	26.125

Digits	B1	Complete	FacMiss
20	11000	23.822	0.000%
25	50000	3.021	4.875%
30	250000	0.287	75.083%
35	1000000	0.022	97.834%
40	3000000	0.001	99.860%

ECM Summary

B1	B2	factor	curves	GHz-days
		56528943437083617060023	1	0.00000e+0
50000	5000000		279	4.482
250000	25000000		144	11.57

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2007-08-30T09:18:00	Team_Bundu	bundu1	50000	5000000						1	0.016
2007-10-20T23:09:00	Andi47	Core2Duo	50000	5000000						1	0.016
2008-01-11T10:01:00	Team_Bundu	bundu1			56528943437083617060023	75.581		1		1	-
2015-06-12T09:29:00	TJAOI	Manual testing	50000	5000000						96	1.542
2016-02-19T14:33:50	TJAOI	Manual testing	50000	5000000						90	1.446
2016-09-09T13:48:13	TJAOI	Manual testing	50000	5000000						91	1.462
2018-04-13T12:45:47	TJAOI	Manual testing	250000	25000000						44	3.534
2020-11-27T10:31:10	TJAOI	Manual testing	250000	25000000						100	8.032

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
2002-04-07T00:00:00	ANONYMOUS	v4_computers	B0BA348B550008__	0.007

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-27T09:32:22

Oliver Kruse

GTX-2

56528943437083617060023

32DA7A0FCA82EC__

2017-09-28T09:42:21

Oliver Kruse

Manual testing

56528943437083617060023

32DA7A0FCA82EC__

2017-11-09T04:46:07

kkmrkkblmbrbk

c4.large

56528943437083617060023

32DA7A0FCA82EC__

2020-04-19T00:22:26

Oliver Kruse

AddPrpType5

56528943437083617060023

6E1250668E07B1__

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 = 10000000, B2 = 830000000 (P-1 stage 2)

B1 = 10000000 (P-1 stage 1)

B1 = 1500000, B2 = 50000000 (P-1 stage 2)

B1 = 1500000 (P-1 stage 1)

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

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

B1 = 100000, B2 = 4000000 (P-1 stage 2)

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

B1 = 131072 (P-1 stage 1)

B1 = 100000 (P-1 stage 1)

B1 = 65536 (P-1 stage 1)

B1 = 32768 (P-1 stage 1)

10³

10⁴

10⁵

10⁶

10⁷

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

TF factor-bounds graph:

2⁶⁷

2⁵⁸

2⁵⁷

2⁵⁶

2⁵⁵

2⁵⁴

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

Last modified: 2022-03-07T07:41:58+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