M675839 Mersenne number exponent details

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M675839

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is 2 ⁶⁷⁵⁸³⁹ - 1

has 203448 decimal digits

takes 0.013 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	CB3096362CBF84__	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	43.9660	70.1493%	1000000	30000000	0.0747	5.5351%	44.0407	71.8015%	1.6523%
PrimeNet	2⁴⁰	0.0000	50.0000%	6500	240000	0.0006	21.1580%	0.0006	60.5790%	10.5790%
GPU72	2⁴⁴	0.0000	54.5455%	11000	400000	0.0009	16.0310%	0.0009	61.8323%	7.2868%
Difference	+23	+43.9660	+15.6038%	+989000	+29600000	+0.0738	-10.4959%	+44.0398	+9.9692%	+9.9692%

Known prime factors (2 factors, 149.9 bits, 0.02218092% 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
675839	5086090084696879369	19	62.141	3762797119356 2² × 3 × 11 × 28506038783	2007-12-06	11	28506038783	2.2785	44.977	84.004
675839	263159078697342977247933143	27	87.766	194690657610276247189 7 × 11 × 109 × 233 × 99557038186981	2015-10-16	233	99557038186981	59,516,309	157,082	293,385

1 Composite Factors:

exponent	prime factors	composite factor	digits	bits*
675839	5086090084696879369 263159078697342977247933143	1338450780860521886436976084068375017248026767	46	149.907

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		-		-	-	0.009	-	-	2.614%
2002-05-11T00:00:00	ANONYMOUS	v4_computers	16384	1638400		-		-	-	0.003	-	-	1.232%
2002-07-06T00:00:00	ANONYMOUS	v4_computers	32768	3276800		-		-	-	0.006	-	-	1.854%
2002-10-19T00:00:00	ANONYMOUS	v4_computers	65536	6553600		-		-	-	0.012	-	-	2.617%
2003-06-17T00:00:00	ANONYMOUS	v4_computers	131072	13107200		-		-	-	0.024	-	-	3.507%
unknown			1000000	30000000		-		-	-	0.075	-	-	5.535%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2001-04-08T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁶		-	-	0.014	-	-
2002-01-02T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁷		-	-	0.028	-	-
2003-10-14T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.057	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	11.243 GHz-days
Estimated T-Level:	25.344

Digits	B1	Curves	Complete	FacMiss
20	11000	324 / 100	3.240	3.853%
25	50000	324 / 280	1.157	31.373%
30	250000	44 / 640	0.069	93.351%

New Calculation Method

Total ECM effort:	11.243 GHz-days
Estimated T-Level:	25.344

Digits	B1	Complete	FacMiss
20	11000	14.769	0.000%
25	50000	1.616	19.866%
30	250000	0.131	87.697%
35	1000000	0.009	99.130%

ECM Summary

B1	B2	factor	curves	GHz-days
		5086090084696879369	1	0.00000e+0
50000	5000000		224	5.037
50000	5000000	263159078697342977247933143	56	1.259
250000	25000000		44	4.947

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2007-08-27T15:26:00	Chad Davis	Bayes	50000	5000000						1	0.022
2007-12-02T06:14:00	Andi47	Core2Duo	50000	5000000						1	0.022
2007-12-02T07:38:00	James Heinrich	WHS	50000	5000000						1	0.022
2007-12-02T12:15:00	Andi47	Core2Duo	50000	5000000						1	0.022
2007-12-06T21:25:00	James Heinrich	WHS			5086090084696879369	62.141		1		1	-
2015-10-16T10:45:17	TJAOI	Manual testing	50000	5000000	263159078697342977247933143	87.766	56	2		56	1.259
2015-10-23T13:49:35	TJAOI	Manual testing	50000	5000000						39	0.877
2016-05-27T13:51:27	TJAOI	Manual testing	50000	5000000						90	2.024
2017-04-14T13:39:31	TJAOI	Manual testing	50000	5000000						91	2.046
2019-08-26T13:37:58	TJAOI	Manual testing	250000	25000000						44	4.947

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
2002-10-19T00:00:00	ANONYMOUS	v4_computers	CB3096362CBF84__	0.013

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-27T14:50:45

Oliver Kruse

GTX-3

5086090084696879369

263159078697342977247933143

80A55BFC656E9285

2017-09-28T09:45:04

Oliver Kruse

Manual testing

5086090084696879369

263159078697342977247933143

80A55BFC656E92__

2017-09-30T15:29:21

alpertron

Manual testing

5086090084696879369

263159078697342977247933143

80A55BFC656E92__

2017-12-08T07:38:57

ATH

xps

5086090084696879369

263159078697342977247933143

80A55BFC656E92__

2020-04-20T02:24:08

Oliver Kruse

AddPrpType5

5086090084696879369

263159078697342977247933143

A69D65E3D5C930__

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 = 30000000 (P-1 stage 2)

B1 = 1000000 (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)

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TF factor-bounds graph:

2⁶⁷

2⁵⁸

2⁵⁷

2⁵⁶

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

Last modified: 2020-04-20T02:24:08+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