M2608873 Mersenne number exponent details

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M2608873

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>>>

is 2 ^2608873 - 1

has 785350 decimal digits

takes 0.181 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	777D2BF6B55CE160	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	2⁶⁸	22.8470	67.6471%	3000000	90000000	0.7784	7.7818%	23.6254	70.1647%	2.5176%
PrimeNet	2⁵⁹	0.0294	62.7119%	11000	200000	0.0021	2.6966%	0.0316	63.7174%	1.0055%
GPU72	2⁶³	0.6118	65.0794%	12000	200000	0.0022	1.5314%	0.6140	65.6141%	0.5348%
Difference	+5	+22.2352	+2.5677%	+2988000	+89800000	+0.7762	+6.2504%	+23.0114	+4.5506%	+4.5506%

Known prime factors (1 factor, 82.6 bits, 0.00316562% 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
2608873	7264176009815521492404503	25	82.587	1392205755093391187 277 × 5026013556293831	2020-07-05	277	5026013556293831	584,040	27,540,181	51,437,388

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2003-10-31T00:00:00	ANONYMOUS	v4_computers	2048	204800		-		-	-	0.001	-	-	0.238%
2003-11-08T00:00:00	Team Prime Rib	v4_computers	15000	217500		-		-	-	0.003	-	-	0.781%
2010-11-17T11:34:00	Jocelyn Larouche	Manual testing	20000	20000		-		-	-	0.002	-	-	0.266%
2010-12-15T10:17:00	markr	tiny	100000	2125000		-		-	-	0.021	-	-	2.472%
2014-10-10T20:28:00	Jocelyn Larouche	Manual testing	124602	124602		-		-	-	0.013	-	-	0.941%
2016-05-19T05:28:34	Jocelyn Larouche	Manual testing	200000	3600000	6	-		-	-	0.039	-	-	3.154%
2017-07-10T01:11:34	Jocelyn Larouche	low 4M	400000	4000000	6	-		-	-	0.060	-	-	3.545%
2019-12-03T14:18:39	masser	Manual testing	2000000	50000000	12	-		-	-	0.464	-	-	6.847%
2019-12-05T17:16:50	BigBrother	Winston	3000000	90000000	12	-		-	-	0.778	-	-	7.782%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1999-03-26T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁹		-	-	0.029	-	-
2016-02-23T16:29:17	Mark Rose	Manual testing	2⁵⁹	2⁶⁰		-	-	0.029	-	-
2009-01-31T14:34:00	Sturle Sunde	ghia.ifi	2⁶⁰	2⁶¹		-	-	0.059	-	-
2012-06-29T19:48:00	Grant McCracken	thumper	2⁶¹	2⁶²		-	-	0.118	-	-
2013-01-14T11:55:00	dbaugh	Manual testing	2⁶²	2⁶³		-	-	0.376	-	-
2015-02-18T11:41:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.753	-	-
2015-02-18T11:41:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.432	-	-
2016-01-15T14:57:04	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	2.864	-	-
2017-08-24T10:53:49	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	5.729	-	-
2019-05-06T12:23:23	TJAOI	Manual testing	2⁶⁷	2⁶⁸		-	-	11.46	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	3.238 GHz-days
Estimated T-Level:	1.750

Digits	B1	Curves	Complete	FacMiss
20	11000	35 / 100	0.350	70.345%
25	50000	35 / 280	0.125	88.230%

New Calculation Method

Total ECM effort:	3.238 GHz-days
Estimated T-Level:	1.750

Digits	B1	Complete	FacMiss
20	11000	1.129	32.335%
25	50000	0.102	90.299%
30	250000	0.006	99.374%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		33	3.053
50000	5000000	7264176009815521492404503	2	0.185

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-02-25T17:39:00	Sturle Sunde	v26	50000	5000000						3	0.278
2010-06-06T13:38:00	James Hintz	ryan	50000	5000000						3	0.278
2012-11-18T13:36:00	Donna Noble	PH2x6	50000	5000000						3	0.278
2014-08-24T22:07:00	Bruce	xps630	50000	5000000						3	0.278
2015-11-16T11:06:40	lopper	i5-4670	50000	5000000						3	0.278
2016-03-23T13:16:27	Jason U	Server7	50000	5000000						3	0.278
2016-08-16T19:12:49	ANONYMOUS	ford7619	50000	5000000						3	0.278
2017-06-10T09:34:20	Bruce	eleven	50000	5000000						3	0.278
2017-10-22T13:47:33	Chang Chia-Tche	ex-ctcpc	50000	5000000						3	0.278
2018-04-18T05:43:46	deo2016	VPS_001	50000	5000000						3	0.278
2019-02-23T20:17:29	-Anonymous-		50000	5000000						3	0.278
2020-07-05T06:08:24	GAN	LMS-11	50000	5000000	7264176009815521492404503	82.587	2	2	7914784071221266	2	0.185

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1999-04-23T00:00:00	ANONYMOUS	v4_computers	777D2BF6B55CE160	0.181
2018-06-28T21:28:00	kkmrkkblmbrbk	old	777D2BF6B55CE160	0.181

PRP results:

date

userid

compid

cofactors

res64

PRP

2020-07-05T08:47:01

Christoph Zenger

Manual testing

7264176009815521492404503

5A436610D9257718

2020-07-05T10:14:35

CrypticClue

cruncher

7264176009815521492404503

5A436610D9257718

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 = 90000000 (P-1 stage 2)

B1 = 2000000, B2 = 50000000 (P-1 stage 2)

B1 = 3000000 (P-1 stage 1)

B1 = 2000000 (P-1 stage 1)

B1 = 400000, B2 = 4000000 (P-1 stage 2)

B1 = 400000 (P-1 stage 1)

B1 = 200000, B2 = 3600000 (P-1 stage 2)

B1 = 100000, B2 = 2125000 (P-1 stage 2)

B1 = 200000 (P-1 stage 1)

B1 = 124602 (P-1 stage 1)

B1 = 100000 (P-1 stage 1)

B1 = 15000, B2 = 217500 (P-1 stage 2)

B1 = 20000 (P-1 stage 1)

B1 = 15000 (P-1 stage 1)

B1 = 2048, B2 = 204800 (P-1 stage 2)

B1 = 2048 (P-1 stage 1)

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

10¹²

10¹³

10¹⁴

10¹⁵

10¹⁶

TF factor-bounds graph:

2⁶⁸

2⁶⁷

2⁶⁶

2⁶⁵

2⁶⁴

2⁶³

2⁶²

2⁶¹

2⁶⁰

2⁵⁹

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

Last modified: 2020-07-05T10:14:35+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