M566707 Mersenne number exponent details

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M566707

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is 2 ⁵⁶⁶⁷⁰⁷ - 1

has 170596 decimal digits

takes 0.008 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	DF68A7CFCE5BB5__	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	52.4326	70.1493%	1500000	50000000	0.0876	6.1830%	52.5202	71.9949%	1.8457%
PrimeNet	2⁴⁰	0.0000	50.0000%	5500	200000	0.0003	19.9867%	0.0003	59.9934%	9.9934%
GPU72	2⁴⁴	0.0000	54.5455%	10000	340000	0.0006	15.1859%	0.0006	61.4481%	6.9027%
Difference	+23	+52.4326	+15.6038%	+1490000	+49660000	+0.0870	-9.0028%	+52.5196	+10.5468%	+10.5468%

Known prime factors (1 factor, 86.0 bits, 0.01517183% 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
566707	76297210055925392603761369	26	85.980	67316276361440208612 2² × 3 × 97217293 × 57702591007	2008-01-21	97217293	57702591007	16,735,796	68.422	124.16

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2001-12-22T00:00:00	ANONYMOUS	v4_computers	2000	200000		-		-	-	0.000	-	-	0.184%
2002-01-22T00:00:00	ANONYMOUS	v4_computers	4096	409600		-		-	-	0.001	-	-	0.398%
2002-03-03T00:00:00	ANONYMOUS	v4_computers	8192	819200		-		-	-	0.001	-	-	0.726%
2002-04-28T00:00:00	ANONYMOUS	v4_computers	16384	1638400		-		-	-	0.002	-	-	1.189%
2002-05-11T00:00:00	ANONYMOUS	v4_computers	50000	1000000		-		-	-	0.002	-	-	1.542%
2002-06-29T00:00:00	ANONYMOUS	v4_computers	32768	3276800		-		-	-	0.004	-	-	1.797%
2002-09-14T00:00:00	ANONYMOUS	v4_computers	65536	6553600		-		-	-	0.009	-	-	2.545%
2003-05-19T00:00:00	ANONYMOUS	v4_computers	131072	13107200		-		-	-	0.018	-	-	3.421%
unknown			1500000	50000000		-		-	-	0.088	-	-	6.183%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2000-04-05T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁴		-	-	0.004	-	-
2022-03-07T08:27:29	LordJulius	Manual testing	2⁵⁴	2⁵⁵		-	-	0.004	-	-
2001-04-08T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁶		-	-	0.017	-	-
2002-01-22T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁷		-	-	0.034	-	-
2003-12-02T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.068	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	17.296 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:	17.296 GHz-days
Estimated T-Level:	26.125

Digits	B1	Complete	FacMiss
20	11000	24.731	0.000%
25	50000	3.128	4.382%
30	250000	0.300	74.084%
35	1000000	0.023	97.713%
40	3000000	0.001	99.851%

ECM Summary

B1	B2	factor	curves	GHz-days
		76297210055925392603761369	1	0.00000e+0
50000	5000000		279	4.517
250000	25000000		44	3.562
250000	35000000		100	9.217

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2007-08-20T09:34:00	Chad Davis	Bayes	50000	5000000						1	0.016
2007-09-27T23:55:00	ANONYMOUS	minister	50000	5000000						1	0.016
2008-01-21T17:00:00	Team_Bundu	bundu3			76297210055925392603761369	85.980		1		1	-
2015-06-06T07:36:00	Richard B. Woods	Puttputt	50000	5000000						1	0.016
2015-08-14T10:08:00	TJAOI	Manual testing	50000	5000000						96	1.554
2016-03-18T10:48:31	TJAOI	Manual testing	50000	5000000						89	1.441
2016-10-21T13:21:14	TJAOI	Manual testing	50000	5000000						91	1.473
2019-03-22T12:39:24	TJAOI	Manual testing	250000	25000000						44	3.562
2021-04-09T16:07:50	TJAOI	Manual testing	250000	35000000						100	9.217

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
2002-06-09T00:00:00	ANONYMOUS	v4_computers	DF68A7CFCE5BB5__	0.008

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-27T11:14:41

Oliver Kruse

GTX-3

76297210055925392603761369

FFF909DA3B3B1F__

2017-09-28T09:43:24

Oliver Kruse

Manual testing

76297210055925392603761369

FFF909DA3B3B1F__

2017-11-07T17:09:57

kkmrkkblmbrbk

c4.xlarge

76297210055925392603761369

FFF909DA3B3B1F__

2020-04-19T08:02:34

Oliver Kruse

AddPrpType5

76297210055925392603761369

163E6E5E3041BC__

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

B1 = 131072 (P-1 stage 1)

B1 = 16384, B2 = 1638400 (P-1 stage 2)

B1 = 50000, B2 = 1000000 (P-1 stage 2)

B1 = 65536 (P-1 stage 1)

B1 = 8192, B2 = 819200 (P-1 stage 2)

B1 = 50000 (P-1 stage 1)

B1 = 32768 (P-1 stage 1)

B1 = 4096, B2 = 409600 (P-1 stage 2)

B1 = 16384 (P-1 stage 1)

B1 = 2000, B2 = 200000 (P-1 stage 2)

B1 = 8192 (P-1 stage 1)

B1 = 4096 (P-1 stage 1)

B1 = 2000 (P-1 stage 1)

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

TF factor-bounds graph:

2⁶⁷

2⁵⁸

2⁵⁷

2⁵⁶

2⁵⁵

2⁵⁴

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

Last modified: 2022-03-07T08:27:29+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