M3202799 Mersenne number exponent details

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M3202799

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>>>

is 2 ^3202799 - 1

has 964139 decimal digits

takes 0.273 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	D4B4D4F1ABA4E144	double-checked
PRP	7DF3E10275084206	verified PRP

	Trial Factoring			P-1 Factoring				Combined
	Limit	GHz-days	Probability	B1	B2	GHz-days	Probability	GHz-days	Probability	Prob over default TF
Actual	2⁶⁹	37.2758	68.1159%	4000000	150000000	1.4753	8.0992%	38.7511	70.6983%	2.5824%
PrimeNet	2⁶⁰	0.0480	63.3333%	13000	240000	0.0031	2.6579%	0.0511	64.3079%	0.9745%
GPU72	2⁶⁴	1.1113	65.6250%	16000	260000	0.0036	1.6160%	1.1149	66.1805%	0.5555%
Difference	+5	+36.1645	+2.4909%	+3984000	+149740000	+1.4717	+6.4833%	+37.6362	+4.5178%	+4.5178%

Known prime factors (1 factor, 77.9 bits, 0.00243082% 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
3202799	273190791577439316158153	24	77.854	42648756849468124 2² × 4349 × 7433 × 329832043	2021-02-24	7433	329832043	9,813.2	2.2186	4.1421

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2008-11-20T01:15:00	Matthias Wurtinger	Manual testing	131072	131072		-		-	-	0.016	-	-	0.875%
2010-10-02T00:00:00	ANONYMOUS	v4_computers	95000	1805000		-		-	-	0.023	-	-	2.153%
2011-11-28T20:59:00	harlee	P4_2600	210000	5040000		-		-	-	0.058	-	-	3.158%
2018-08-06T19:37:33	Jocelyn Larouche	low 4M	420000	840000		-		-	-	0.055	-	-	2.101%
2018-08-07T17:09:34	Jocelyn Larouche	low 4M	420000	1260000		-		-	-	0.057	-	-	2.407%
2018-08-13T19:32:42	Jocelyn Larouche	low 4M	420000	2940000		-		-	-	0.069	-	-	3.059%
2018-08-14T23:01:50	Jocelyn Larouche	low 4M	420000	3360000		-		-	-	0.072	-	-	3.163%
2018-08-15T10:51:05	Jocelyn Larouche	low 4M	420000	3780000		-		-	-	0.074	-	-	3.256%
2019-12-18T06:38:25	mikr	MSI	4000000	150000000	12	-		-	-	1.475	-	-	8.099%
2022-03-11T08:07:53	Jocelyn Larouche	Manual testing	1000000	134343300		-		-	-	1.020	-	-	6.999%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1998-01-13T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁹		-	-	0.024	-	-
2001-05-27T00:00:00	ANONYMOUS	v4_computers	2¹	2⁶⁰		-	-	0.048	-	-
2008-11-22T12:51:00	Matthias Wurtinger	WUR_E6600	2⁶⁰	2⁶¹		-	-	0.048	-	-
2008-11-22T12:53:00	Matthias Wurtinger	WUR_E6600	2⁶¹	2⁶²		-	-	0.096	-	-
2013-01-03T08:47:00	dbaugh	Manual testing	2⁶²	2⁶³		-	-	0.306	-	-
2015-02-15T12:51:00	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.613	-	-
2015-02-15T12:51:00	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.167	-	-
2015-06-21T21:40:00	Tha	Manual testing	2⁶⁵	2⁶⁶		-	-	2.333	-	-
2017-03-15T13:25:42	Gordon Spence	Manual testing	2⁶⁶	2⁶⁷		-	-	4.666	-	-
2019-01-28T14:25:40	TJAOI	Manual testing	2⁶⁷	2⁶⁸		-	-	9.333	-	-
2021-01-27T17:52:57	ViliamF	Manual testing	2⁶⁸	2⁶⁹		-	-	18.67	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	4.283 GHz-days
Estimated T-Level:	1.600

Digits	B1	Curves	Complete	FacMiss
20	11000	32 / 100	0.320	72.498%
25	50000	32 / 280	0.114	89.182%

New Calculation Method

Total ECM effort:	4.283 GHz-days
Estimated T-Level:	1.600

Digits	B1	Complete	FacMiss
20	11000	1.109	32.987%
25	50000	0.103	90.181%
30	250000	0.007	99.336%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		22	2.585
50000	5000000	273190791577439316158153	5	0.587
80000	11280000		5	1.112

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-05-09T02:41:00	Ryan Schulz	T7400	50000	5000000						3	0.352
2011-08-29T10:15:00	Kamil_Górski	thefault	50000	5000000						3	0.352
2014-04-29T07:16:00	Pool Party	St.P.p	50000	5000000						3	0.352
2016-07-28T06:50:45	nokno	leo234	50000	5000000						3	0.352
2018-08-05T18:53:40	IanGlencross	glenx24	50000	5000000						3	0.352
2020-12-21T11:26:46	Zenzoma	AMD3970X	50000	5000000						7	0.822
2021-01-10T02:09:17	axn	Manual testing	80000	11280000						5	1.112
2021-02-24T00:36:41	mnd9	25836b	50000	5000000	273190791577439316158153	77.854	5	2	5416928666034043	5	0.587

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1998-01-13T00:00:00	ANONYMOUS	v4_computers	D4B4D4F1ABA4E144	0.273
1999-06-06T00:00:00	ANONYMOUS	v4_computers	D4B4D4F1ABA4E144	0.273

PRP results:

date

userid

compid

cofactors

res64

PRP

2021-02-25T18:10:29

Cork

3tits

273190791577439316158153

7DF3E10275084206

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 = 4000000, B2 = 150000000 (P-1 stage 2)

B1 = 1000000, B2 = 134343300 (P-1 stage 2)

B1 = 4000000 (P-1 stage 1)

B1 = 1000000 (P-1 stage 1)

B1 = 420000, B2 = 3780000 (P-1 stage 2)

B1 = 420000, B2 = 3360000 (P-1 stage 2)

B1 = 420000, B2 = 2940000 (P-1 stage 2)

B1 = 210000, B2 = 5040000 (P-1 stage 2)

B1 = 420000, B2 = 1260000 (P-1 stage 2)

B1 = 420000, B2 = 840000 (P-1 stage 2)

B1 = 420000 (P-1 stage 1)

B1 = 210000 (P-1 stage 1)

B1 = 95000, B2 = 1805000 (P-1 stage 2)

B1 = 131072 (P-1 stage 1)

B1 = 95000 (P-1 stage 1)

10²

10³

10⁴

10⁵

10⁶

10⁷

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

TF factor-bounds graph:

2⁶⁹

2⁶⁸

2⁶⁷

2⁶⁶

2⁶⁵

2⁶⁴

2⁶³

2⁶²

2⁶¹

2⁶⁰

2⁵⁹

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

Last modified: 2022-03-11T08:07:53+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