M563039 Mersenne number exponent details

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M563039

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is 2 ⁵⁶³⁰³⁹ - 1

has 169492 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	0724FB8CEB9DE4__	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	52.7742	70.1493%	15000000	1815000000	2.3909	12.1767%	55.1651	73.7841%	3.6348%
PrimeNet	2⁴⁰	0.0000	50.0000%	5500	200000	0.0003	19.9719%	0.0003	59.9860%	9.9860%
GPU72	2⁴⁴	0.0000	54.5455%	10000	340000	0.0006	15.1740%	0.0006	61.4427%	6.8973%
Difference	+23	+52.7742	+15.6038%	+14990000	+1814660000	+2.3903	-2.9973%	+55.1645	+12.3414%	+12.3414%

Known prime factors (1 factor, 77.3 bits, 0.01373417% 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
563039	189788937447521072597089	24	77.329	168539779169401296 2⁴ × 3 × 19 × 184802389440133	2007-08-20	19	184802389440133	86,556	212,908	397,652

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2000-12-31T00:00:00	Alex Kruppa	v4_computers	2000	40000		-		-	-	8.60708e-5	-	-	0.107%
2001-07-17T00:00:00	Alex Kruppa	v4_computers	100000	4000000		-		-	-	0.007	-	-	2.543%
2002-05-05T00:00:00	ANONYMOUS	v4_computers	16384	1638400		-		-	-	0.002	-	-	1.188%
2002-06-29T00:00:00	ANONYMOUS	v4_computers	32768	3276800		-		-	-	0.004	-	-	1.795%
2002-09-14T00:00:00	ANONYMOUS	v4_computers	65536	6553600		-		-	-	0.009	-	-	2.542%
2003-05-19T00:00:00	ANONYMOUS	v4_computers	131072	13107200		-		-	-	0.018	-	-	3.417%
2021-08-28T10:32:11	ViliamF	3	15000000	1815000000		-		-	-	2.391	-	-	12.177%

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	-	-
2022-03-07T08:27:24	LordJulius	Manual testing	2⁵⁴	2⁵⁵		-	-	0.004	-	-
2001-04-08T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁶		-	-	0.017	-	-
2002-01-15T00:00:00	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:	16.199 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:	16.199 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
		189788937447521072597089	1	0.00000e+0
50000	5000000		281	4.547
250000	25000000		144	11.65

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2007-08-20T04:25:00	Chad Davis	Bayes			189788937447521072597089	77.329		1		1	-
2015-06-02T09:26:00	Richard B. Woods	Puttputt	50000	5000000						1	0.016
2015-07-31T09:47:00	TJAOI	Manual testing	50000	5000000						100	1.618
2016-03-24T20:24:33	TJAOI	Manual testing	50000	5000000						89	1.440
2016-09-23T16:22:45	TJAOI	Manual testing	50000	5000000						91	1.473
2019-04-12T15:18:55	TJAOI	Manual testing	250000	25000000						44	3.560
2021-03-05T18:04:23	TJAOI	Manual testing	250000	25000000						100	8.091

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
2002-05-25T00:00:00	ANONYMOUS	v4_computers	0724FB8CEB9DE4__	0.008

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-27T11:07:27

Oliver Kruse

GTX-2

189788937447521072597089

58770168601CED__

2017-09-28T09:43:17

Oliver Kruse

Manual testing

189788937447521072597089

58770168601CED__

2017-11-07T06:54:22

kkmrkkblmbrbk

c4.xlarge

189788937447521072597089

58770168601CED__

2020-04-19T07:42:10

Oliver Kruse

AddPrpType5

189788937447521072597089

C36EBEFE5110C9__

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 = 15000000, B2 = 1815000000 (P-1 stage 2)

B1 = 15000000 (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 = 16384, B2 = 1638400 (P-1 stage 2)

B1 = 100000 (P-1 stage 1)

B1 = 65536 (P-1 stage 1)

B1 = 32768 (P-1 stage 1)

B1 = 16384 (P-1 stage 1)

B1 = 2000, B2 = 40000 (P-1 stage 2)

B1 = 2000 (P-1 stage 1)

10⁰

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10¹

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10⁴

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TF factor-bounds graph:

2⁶⁷

2⁵⁸

2⁵⁷

2⁵⁶

2⁵⁵

2⁵⁴

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

Last modified: 2022-03-07T08:27:24+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