M4323691 Mersenne number exponent details

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M4323691

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is 2 ^4323691 - 1

has 1301561 decimal digits

takes 0.539 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	A6BAACC264AEE1A8	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	2⁷³	442.4100	68.4932%	440000	13200000	0.2053	2.9707%	442.6153	69.4291%	0.9360%
PrimeNet	2⁶¹	0.0710	62.2951%	18000	360000	0.0066	2.9286%	0.0777	63.3993%	1.1042%
GPU72	2⁶⁵	1.6874	64.6154%	24000	500000	0.0090	1.9837%	1.6964	65.3173%	0.7019%
Difference	+8	+440.7227	+3.8778%	+416000	+12700000	+0.1963	+0.9870%	+440.9189	+4.1118%	+4.1118%

Known prime factors:
No known factors for M4323691

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2001-06-03T00:00:00	Team_Deutschland	v4_computers	20000	180000		-		-	-	0.005	-	-	0.412%
2010-09-01T17:57:00	markr	tiny	95000	2090000		-		-	-	0.037	-	-	1.425%
2016-12-24T16:54:39	Squeeky_Squirrel	P4_2600	265000	7751250	12	-		-	-	0.122	-	-	2.431%
2021-06-13T04:39:25	Dylan Delgado	Manual testing	440000	13200000	12	-		-	-	0.205	-	-	2.971%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1998-02-01T00:00:00	Sturle Sunde	v4_computers	2¹	2⁶⁰		-	-	0.036	-	-
1998-09-13T00:00:00	ANONYMOUS	v4_computers	2¹	2⁶¹		-	-	0.071	-	-
2010-12-06T20:25:00	markr	oldgamer	2⁶¹	2⁶²		-	-	0.071	-	-
2012-01-08T22:25:00	GrunwalderGIMP	Manual testing	2¹	2⁶³		-	-	0.369	-	-
2016-02-23T16:29:53	Mark Rose	Manual testing	2⁶²	2⁶³		-	-	0.227	-	-
2014-05-29T22:24:00	Jayder	Manual testing	2⁶³	2⁶⁴		-	-	0.454	-	-
2014-05-30T07:44:00	lycorn	Manual testing	2⁶⁴	2⁶⁵		-	-	0.864	-	-
2015-06-15T10:06:00	snme2pm1	Manual testing	2⁶⁵	2⁶⁶		-	-	1.728	-	-
2018-04-30T04:51:03	chuenkit	Manual testing	2⁶⁶	2⁶⁷		-	-	3.457	-	-
2018-10-24T03:13:30	chuenkit	Manual testing	2⁶⁷	2⁶⁸		-	-	6.913	-	-
2021-01-26T02:19:37	-Anonymous-	Manual testing	2⁶⁸	2⁶⁹		-	-	13.83	-	-
2021-01-26T02:19:38	-Anonymous-	Manual testing	2⁶⁹	2⁷⁰		-	-	27.65	-	-
2021-01-30T18:20:09	-Anonymous-	Manual testing	2⁷⁰	2⁷¹		-	-	55.31	-	-
2021-01-30T18:20:09	-Anonymous-	Manual testing	2⁷¹	2⁷²		-	-	110.6	-	-
2021-02-10T11:27:35	-Anonymous-	Manual testing	2⁷²	2⁷³		-	-	221.2	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	2.197 GHz-days
Estimated T-Level:	0.600

Digits	B1	Curves	Complete	FacMiss
20	11000	12 / 100	0.120	88.638%
25	50000	12 / 280	0.043	95.797%

New Calculation Method

Total ECM effort:	2.197 GHz-days
Estimated T-Level:	0.600

Digits	B1	Complete	FacMiss
20	11000	0.462	63.031%
25	50000	0.043	95.819%
30	250000	0.003	99.731%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		12	2.197

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-12-15T04:57:00	S00030	vd01	50000	5000000						3	0.549
2013-03-15T01:57:00	Kish	HPtower-office	50000	5000000						3	0.549
2016-07-26T10:43:04	Bruce	desk	50000	5000000						3	0.549
2019-06-02T11:12:42	furkell	furkell1	50000	5000000						3	0.549

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1998-11-21T00:00:00	ANONYMOUS	v4_computers	8A209C03784978__	0.539
1999-11-04T00:00:00	ANONYMOUS	v4_computers	A6BAACC264AEE1A8	0.539
2001-07-03T00:00:00	Team_Deutschland	v4_computers	A6BAACC264AEE1A8	0.539

PRP results:
No PRP results for M4323691

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 = 440000, B2 = 13200000 (P-1 stage 2)

B1 = 265000, B2 = 7751250 (P-1 stage 2)

B1 = 440000 (P-1 stage 1)

B1 = 265000 (P-1 stage 1)

B1 = 95000, B2 = 2090000 (P-1 stage 2)

B1 = 95000 (P-1 stage 1)

B1 = 20000, B2 = 180000 (P-1 stage 2)

B1 = 20000 (P-1 stage 1)

10³

10⁴

10⁵

10⁶

10³

10⁴

10⁵

10⁶

10⁷

10⁸

TF factor-bounds graph:

2⁷³

2⁷²

2⁷¹

2⁷⁰

2⁶⁹

2⁶⁸

2⁶⁷

2⁶⁶

2⁶⁵

2⁶⁴

2⁶³

2⁶²

2⁶¹

2⁶⁰

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

Last modified: 2021-06-13T04:39:25+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